.TI-83, TI-83 Plus, TI-84 Plus Guide Guide for Texas Instruments TI-83, TI-83 Plus, or TI-84 Plus Graphing Calculator This Guide is designed to offer step-by-step instruction for using your TI-83, TI-83 Plus, or TI-84 Plus graphing calculator with the fourth edition of Calculus Concepts: An Informal Approach to the Mathematics of Change.TI-83, TI-83 Plus, TI-84 Plus Guide Basic Operation You should be familiar with the basic operation of your calculator. With your calculator in hand, go through each of the following.

1. Texas Instruments Ti 82 Instructions
2. Manual De Calculadora Texas Instruments Ti-82 Manual

CALCULATING You can type in lengthy expressions; just be certain that you use parentheses to control the calculator's order of operations.TI-83, TI-83 Plus, TI-84 Plus Guide The “to a fraction” key is obtained by pressing MATH 1 Frac. The calculator’s symbol for times 10. Thus, 7.945 means 7.945.10 or 7,945,000,000,000. − 6 − 6 The result means 1.4675. 10, which is the scientific 1.4675.TI-83, TI-83 Plus, TI-84 Plus Guide If you try to store something to a particular memory location that is being used for a different type of object, a DATA error results. Consult either Troubleshooting the TYPE Calculator in this Guide or your particular calulator Owner’s Guidebook.TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 1 Ingredients of Change: Functions and Linear Models 1.1 Models and Functions Graphing a function in an appropriate viewing window is one of the many uses for a function that is entered in the calculator’s graphing list. Because you must enter a function formula on one line, it is important to use parentheses whenever they are needed.Chapter 1 Press to set the view for the graph.

Enter 0 for WINDOW Xmin and 20 for (For 10 tick marks between 0 and 20, enter 2 Xmax. If you want 20 tick marks, enter 1 for etc. Xscl, Xscl does not affect the shape of the graph.TI-83, TI-83 Plus, TI-84 Plus Guide Press and the input value is substituted in the function. ENTER The input and output values are shown at the bottom of the screen.

(This method works even if you do not see any of the graph on the screen.).Chapter 1 EVALUATING OUTPUTS ON THE HOME SCREEN The input values used in the eval- uation process are actual values, not estimated values such as those generally obtained by tracing near a certain value. We again consider the function v(t) = 3.5(1.095 Using x as the input variable, enter.TI-83, TI-83 Plus, TI-84 Plus Guide Press, and observe the list of input GRAPH (TABLE) and output values. Notice that you can scroll through the table with, and/or The table values may be ▼, ▲ ◄ ►.Chapter 1 If you already have in the graphing list, you Y1 = 3.622(1.093^X) can refer to the function as in the If not, you can SOLVER. Enter instead of in the location of the 3.622(1.093^X) eqn: Press SOLVER. If you need to edit the equation, press until the previous ▲.TI-83, TI-83 Plus, TI-84 Plus Guide 1. Enter the function in some location of the graphing list – say and draw a graph of the function.

Press Y1 = 3.5(1.095^X) and hold down either until you have an TRACE ►.Chapter 1 Press and clear all locations with Enter the func- CLEAR. Tion 3x – 0.8x + 4 – 2.3 in. You can enter x with X,T,θ,n or enter it with. Remember to use, not X,T,θ,n ^ 2 −.TI-83, TI-83 Plus, TI-84 Plus Guide Draw the graphs with ZOOM 4 ZDecimal ZOOM 6 If you use the former, press and reset ZStandard. WINDOW to get a better view the graph.

(If you Xmax Ymax reset the window, press to draw the graph.).Chapter 1 Enter to obtain the sum function (f + g)(x) = f(x) + g(x). Y1 + Y2 Enter to obtain the difference function (f – g)(x) = f(x) – g(x). Y1 – Y2 ⋅ ⋅ Enter to obtain the product function (f g)(x) = f(x) Y1.Y2 g(x).TI-83, TI-83 Plus, TI-84 Plus Guide Press and clear each previously entered equation with Y=, Enter M in by pressing CLEAR.

02 X,T,θ,n + 1. And input S in by pressing 90 ENTER. 5 ( ^ X,T,θ,n ) ENTER.Chapter 1 To locate where, press Y1 = Y2 2ND TRACE (CALC) 5 Press to mark the first curve. The cursor intersect. ENTER jumps to the other function – here, the line. Next, press to mark the second curve.

Next, supply a guess for ENTER the point of intersection.TI-83, TI-83 Plus, TI-84 Plus Guide Press and, using one of the arrow keys, move the cursor until it covers the darkened = in. Then, ENTER press until the cursor covers the darkened = in. Press ▼.Chapter 1 In this text, we usually use list for the input data and list for the output data. If there are any data values already in your lists, first delete any “old” data using the following procedure.

(If your lists are clear, skip these instructions.) DELETING OLD DATA Whenever you enter new data in your calculator, you should first delete any previously entered data.TI-83, TI-83 Plus, TI-84 Plus Guide Have the data given in Table 1.1 in Section 1.2 of Calculus Concepts entered in your calculator. Exit the list menu with MODE (QUIT). To run the program, press followed by the number that.Chapter 1. Lists can be named and stored in the calculator’s memory for later recall and use. Refer to p.23 of this Guide for instructions on storing data lists and later recalling them for use. CAUTION: Any time that you enter the name of a numbered list (for instance:, and so forth), you should use the calculator symbol for the name, not a name that you type with the alphabetic and numeric keys.TI-83, TI-83 Plus, TI-84 Plus Guide data were constant at $541, so a linear function fit the data perfectly. What information is given by the first differences for these modified tax data?

Run program by pressing followed by the DIFF.Chapter 1 find a linear function for input data in list and output data in list and paste the equation into graphing location STAT ► CALC 4 LinReg(ax+b) 3 (L3), 2nd 4 (L4), VARS ► Y−VARS 1 Function 2 Y2 ENTER. CAUTION: The r that is shown is called the correlation coefficient.TI-83, TI-83 Plus, TI-84 Plus Guide Press to access the data lists. To copy the con- STAT 1 EDIT tents of one list to another list; for example, to copy the contents, use to move the cursor so that ▲.Chapter 1. There are many ways that you can enter the aligned input into. One method that you may prefer is to start over from the beginning. Replace with the contents of highlighting and pressing Once again highlight the name 2ND 3 (L3) ENTER.TI-83, TI-83 Plus, TI-84 Plus Guide Press to return to the home screen.

You MODE (QUIT) can view any list from the mode (where the data is STAT EDIT originally entered) or from the home screen by typing the name.Chapter 1 Press To delete another list, use to move ENTER. ▼ ▲ the cursor opposite that list name and press Exit this ENTER. Screen with when finished. MODE (QUIT) WARNING: Be careful when in the menu. Once you delete something, it is gone DELETE from the calculator’s memory and cannot be recovered.TI-83, TI-83 Plus, TI-84 Plus Guide Use the tick marks to estimate rise divided by run and note a possible y-intercept. After pressing to resume the ENTER program, enter your guess for the slope and y-intercept. After entering your guess for the y-intercept, your line is drawn and the errors are shown as vertical line segments on the graph.Chapter 1 HAVING THE CALCULATOR ENTER EVENLY SPACED INPUT VALUES When an input list consists of many values that are the same distance apart, there is a calculator command that will generate the list so that you do not have to type the values in one by one.

The syntax for this sequence command is seq(formula, variable, first value, last value, increment).TI-83, TI-83 Plus, TI-84 Plus Guide We continue to use the data in Table 1.17 of the text. Our input data is already small so we need not align to smaller values. Return to the home screen. Following the same procedure that.Chapter 1 Delete (with ) any functions CLEAR that are in the list. A scatter plot of the data drawn with ZOOM 9 shows the slow decline that ZoomStat can indicate a log model.

As when modeling linear and exponential functions, find and paste the log equation into the location of the list by.TI-83, TI-83 Plus, TI-84 Plus Guide using followed by the number of the desired function loca- VARS ► Y−VARS 1 Function tion. The calculator does not recognize as the name of a function in the list.

ALPHA 1 (Y) 1.4 Logistic Functions and Models This section introduces the logistic function that can be used to describe growth that begins as exponential and then slows down to approach a limiting value.Chapter 1 TI-84 Plus.) As you did when finding an exponential equation for data, large input values must be aligned or an error or possibly an incorrect answer could be the result. Note that the calculator finds a “best-fit” logistic function rather than a logistic function with a limiting value L such that no data value is ever greater than L.TI-83, TI-83 Plus, TI-84 Plus Guide RECALLING MODEL PARAMETERS Rounding function parameters can often lead to incorrect or misleading results.

You may find that you need to use the complete values of the coefficients after you have found a function that best fits a set of data. It would be tedious to copy all these digits in a long decimal number into another location of your calculator.Chapter 1 Return to the home screen. Now we find the exponential function and paste the equation into the location of the list by pressing STAT ► CALC 0 ExpReg VARS ► Y−VARS 1 Function 1 Y1. Nvivo 10 crack pes 2016. Press to find the equation and paste it into the ENTER location.TI-83, TI-83 Plus, TI-84 Plus Guide This situation calls for shifting the data vertically so that it ap- proaches a lower asymptote of y = 0,which is what the logistic function in the calculator has as its lower asymptote for an increasing logistic curve.Chapter 1 Press Choose in the WINDOW (TBLSET).

Indpnt: location by placing the cursor over and pressing ENTER. (Remember that the other settings on this screen do not matter if you are using Press Delete any values that appear GRAPH (TABLE).TI-83, TI-83 Plus, TI-84 Plus Guide Have u(x) = in the location of the list. (Be certain that you remember to enclose both the numerator and denominator of the fraction in parentheses.) A graph drawn with is a starting point.Chapter 1 Delete the values currently in the table To numerically estimate u(x), enter values to the right of, and closer and closer − x→ − 2/9. Because the output values appear to become larger and u(x) → − ∞. Larger, we estimate that −.TI-83, TI-83 Plus, TI-84 Plus Guide Draw a graph of h with Press ZOOM 4 ZDecimal. ZOOM 2 and use to move the blinking cursor Zoom In ◄ ▲ − until you are near the point on the graph where x = 1.Chapter 1 Run program and observe the first differences in list DIFF the second differences in, and the percentage differences in list The second differences are close to constant, so a quadratic function may give a good fit for these data. Construct a scatter plot of the data.TI-83, TI-83 Plus, TI-84 Plus Guide First, clear your lists, and then enter the data.

Next, align the input data so that x represents the number of years since 1980. (We do not have to align here, but we do so in order to have smaller coefficients in the cubic function.).Chapter 1 Press to find the input at the point of intersection. ENTER Because x is the number of years after 1980, the answer to the question posed in part c of Example 3 is either 1984 or 1985. The price had not exceeded $6 in 1984, so the answer to the question is 1985.TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 2 Describing Change: Rates As you calculate average and other rates of change, remember that every numerical answer in a context should be accompanied by units telling how the quantity is measured. You should also be able to interpret each numerical answer.Chapter 2 next is type and press. Then, store the next set of inputs into A and/or B and ENTER recall using to recall each instruction.

Press and you ENTER (ENTRY) ENTER have the average rate of change between the two new points. FINDING PERCENTAGE CHANGE You can find percentage changes using data either by the formula or by using program.TI-83, TI-83 Plus, TI-84 Plus Guide Press. An APR of approximately 11.57% ALPHA ENTER compounded monthly will yield $1,000,000 in 40 years on an initial investment of $10,000. We continue with part b of Example 4 of Section 2.1 of Calculus Concepts to illustrate finding the APY that corresponds to an APR of approximately 0.11568.Chapter 2 Use the arrow keys to move the cursor to the opposite corner of your “zoom” box. Point A should be close to the center of your box. Press to magnify the portion of the graph that is inside ENTER the box.TI-83, TI-83 Plus, TI-84 Plus Guide VISUALIZING THE LIMITING PROCESS This section of the Guide is optional, but it might help you understand what it means for the tangent line to be the limiting position of secant lines.

Program is used to view secant lines between a point (a, f(a)) and close SECTAN points on a curve y = f(x).Chapter 2 In this section, we investigate what the calculator does if you ask it to draw a tangent line where the line cannot be drawn. Consider these special cases: 1.

What happens if the tangent line is vertical? We consider the function f(x) = (x + 1) which has a vertical tangent at x = –.TI-83, TI-83 Plus, TI-84 Plus Guide 3a. Clear and enter, as indicated, the function R S ≤ when. (The inequality symbols are when accessed with MATH (TEST).

Set each part of the function to draw in mode by placing the cursor over the equals.Chapter 2 2.3 Derivative Notation and Numerical Estimates CALCULATING PERCENTAGE RATE OF CHANGE Percentage rate of change = rate of change at a point ⋅. We illustrate calculating the percentage rate of change 100% value of the function at that point with the example found on page 134 in Section 2.3 of Calculus Concepts.TI-83, TI-83 Plus, TI-84 Plus Guide Continue in this manner, recording each result on paper, until you can determine to which value the slopes from the left seem to be getting closer and closer. It appears that the slopes of the secant lines from the left are approaching 5.706 billion dollars per year.Chapter 2 many decimal places as are necessary to determine the limit to the desired degree of accuracy.

Note: You may wish to leave the slope formula in as long as you need it. Turn when you are not using it. 2.4 Algebraically Finding Slopes The calculator does not find algebraic formulas for slope, but you can use the built-in numerical derivative and draw the graph of a derivative to check any formula that you find.TI-83, TI-83 Plus, TI-84 Plus Guide Suppose you want to find the slope of the secant line between the points (0, f(0)) and (2, f(2)). That is, you are finding the − − slope of the secant line between the points (a.Chapter 2 These values are those in the fifth row of the above table − the values for k = 0.001.

From this point forward, we use k = 0.001 and therefore do not specify k when evaluating Will nDeriv(. The slope of this secant line always do a good job of approximating the slope of the tangent line when k = 0.001? Yes, it generally does, as long as the instantaneous rate of change exists at the input value at which you evaluate.TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 3 Determining Change: Derivatives 3.3 Exponential and Logarithmic Rate-of-Change Formulas The calculator only approximates numerical values of slopes – it does not give a slope in formula form. You also need to remember that the CALCULATOR calculates the slope (i.e., the derivative) at a specific input value by a different method than the one we use to calculate the slope.Chapter 3 Press and edit to be the function g ( x ) = 2 Access the statistical lists, clear any previous entries from,. Enter the x -values shown above in.

Highlight and enter. Remember to type using Y1(L1) 2ND 1 (L1).TI-83, TI-83 Plus, TI-84 Plus Guide The slope appears at the bottom of the screen.

Dy/dx = 2.0666667 Return to the home screen and press The calculator’s X,T,θ,n. Memory location has been updated to 3.

Now type the numerical derivative instruction (evaluated at 3) as shown to the right.Chapter 3 Start with Neither ZOOM 4 ZDecimal or ZOOM 6 ZStandard. Of these shows a graph (because of the large coefficient in the function), but you can press to see some of the output TRACE values. Using those values, reset the window. The graph to the −.TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 4 Analyzing Change: Applications of Derivatives 4.2 Relative and Absolute Extreme Points Your calculator can be very helpful for checking your analytic work when you find optimal points and points of inflection. When you are not required to show work using derivative formulas or when an approximation to the exact answer is all that is required, it is a simple process to use your calculator to find optimal points and inflection points.Chapter 4 Press to mark the location of the right bound.

You are ENTER next asked to provide a guess. Any value near the intercept will do. Use to move the cursor near the intercept. ◄ Press The location of the x-intercept is displayed.

ENTER.TI-83, TI-83 Plus, TI-84 Plus Guide Reset to a larger value, say 95,000, to better see the high Ymax point on the graph. Graph R and press Hold down TRACE. Until you have an estimate of the input location of the high ►.Chapter 4 Press to mark the left bound of the interval. Use ENTER to move the cursor to the right of the high point on the ► curve. Press to mark the right bound of the interval. Use ENTER to move the cursor to your guess for the high point on the ◄.TI-83, TI-83 Plus, TI-84 Plus Guide Enter f in the location of the list, the first derivative of f, and the second derivative of f in. (Be careful not to round any decimal values.) Turn off We are given the input interval 1982 through 1990, so 0 ≤ x ≤ 8.Chapter 4 Find the x-intercept of the second derivative graph as indicated in this section or find the input of the high point on the first derivative graph (see page 63 of this Guide) to locate the inflection point.

Texas Instruments Ti 82 Instructions

5.3.2 USING THE CALCULATOR TO FIND INFLECTION POINTS Remember that an inflection point on the graph of a function is a point of greatest or least slope.TI-83, TI-83 Plus, TI-84 Plus Guide If you prefer, you could have found the input of the inflection ′′ point by solving the equation C = 0 using the. (Do SOLVER not forget that drawing the graph of C and tracing it can be used.Chapter 5 Chapter 5 Accumulating Change: Limits of Sums and the Definite Integral 5.1 Results of Change and Area Approximations So far, we have used the calculator to investigate rates of change. In this chapter we consider the second main topic in calculus – the accumulation of change. You calculator has many useful features that will assist in your investigations of the results of change.TI-83, TI-83 Plus, TI-84 Plus Guide Consider what is now in the lists. Contains the left endpoints of the 11 rectangles and contains the heights of the rectangles. If we multiply the heights by the widths of the rectan- gles (1 hour) and enter this product in.Chapter 5 With the cursor in, press VARS ► 1 Function 1 Y1 ) ( X,T,θ,n 2ND MATH TEST 6 20 Your calculator draws graphs by connecting function outputs wherever the function is defined.

Manual De Calculadora Texas Instruments Ti-82 Manual

However, this function breaks at x = 20.TI-83, TI-83 Plus, TI-84 Plus Guide AREA APPROXIMATIONS USING RIGHT RECTANGLES We continue with the previous function and find an area approximation using right rectangles. Part a of Example 2 says to find the change in the drug concen- tration from x = 0 through x = 20 using right rectangles of width 2 days.Chapter 5 Clear lists. To use 4 midpoint rectangles to approximate the area of the region between the graph of f and the x-axis between x = 0 and x = 2, first enter the midpoints of the rectangles (0.TI-83, TI-83 Plus, TI-84 Plus Guide Input at the prompt and press A graph of the 4 ENTER. Approximating midpoint rectangles and the function are shown. (Note that the program automatically sets the height of the win- dow based on the left and right endpoints of the input interval.).Chapter 5 We illustrate using this program to find a limit of sums using W(x) = − ⋅ − −, the function in Example 4 of Section 5.1 of 1.243 10 0.0314 2.6174 71.977 Calculus Concepts. Begin by entering the function in Y1.

Notice that to enter −.TI-83, TI-83 Plus, TI-84 Plus Guide Continue in this manner, each time choosing the first option, and doubling until a limit is evident. CHANGE N, Intuitively, finding the limit means that you are sure what the area approximation will be without having to use larger values in the program.Chapter 5. The calculator’s function yields the same result (to 3 decimal places) as that found in fnInt the limit of sums investigation on page 66 of this Guide.

5.3 The Fundamental Theorem of Calculus Intuitively, this theorem tells us that the derivative of an antiderivative of a function is the function itself.TI-83, TI-83 Plus, TI-84 Plus Guide Enter f in, and F in, and fnInt(Y1, X, 0, X), using a different number for C in each function location. (You can use the values of C shown to the right or different values.).Chapter 5 Because part a of Example 3 asks for the areas of the regions above and below the input axis and the function, we must find where the function crosses the axis. You can find this value using the solver (solve = 0) or by using the graph and the x-intercept method described on page A-11 of this guide.TI-83, TI-83 Plus, TI-84 Plus Guide − and draw the graph of with Xmin = 7, Xmax = 0, ZOOM ▲ ZoomFit ENTER. Press The calculator asks TRACE (CALC) 7 ∫f(x)dx. Press and obtain the screen shown to the Lower Limit?

(−).Chapter 5 We next find the inputs of the points of intersection of the two functions. (These values will probably be the limits on the integrals we use to find the areas.) The method we use to find the first of the points is the intersection method that was discussed on page A-11 of this Guide. With the graph on the screen, press TRACE (CALC) 5 The calculator asks.TI-83, TI-83 Plus, TI-84 Plus Guide − NOTE: The value 88 – 3 ≈ 58.8912 could also have been calculated by evaluating fnInt(Y1 − Y2, X, 10, 20). Because the graph in Figure 5.56 shows that the area fnInt(Y1 − Y2, X, 10, 20).Chapter 5 We illustrate for the graph shown above. The area of the rectangle whose height is the average temperature is (3)(1000) ≈ 94,186.472. Using MATH 9 (fnInt), we find that the area of the region between a t = and t = 0 is ≈.TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 6 Analyzing Accumulated Change: Integrals in Action 6.1 Perpetual Accumulation and Improper Integrals NUMERICALLY ESTIMATING END BEHAVIOR Recall from page A-34 of this guide that we can use the calculator to estimate end behavior. We illustrate using the improper ∞.Chapter 6 In Example 1, part a, we are told that the business’s profit remains constant.

In enter two possi- ble input values for the time involved. (You might use different years than the ones shown here.) In enter the amount invested: 10% of the constant profit.TI-83, TI-83 Plus, TI-84 Plus Guide of the data and it should be obvious from the shape of the scatter plot the function to fit to the data. For instance, return to Example 1, part b, in which we are told that the business’s profit grows by $50,000 each year.Chapter 6 To determine the 2-year future value, we add the future value of each month’s deposit, beginning with x = 0 (for month 1) and ending with x = 23 (for month 24).

The calculator sequence command can be used to find this sum. The syntax for this is seq(formula, variable, first value, last value, increment) Return to the home screen and enter seq(Y1, X, 0, 23, 1).TI-83, TI-83 Plus, TI-84 Plus Guide CONSUMER ECONOMICS We illustrate how to find the consumers’ surplus and other economic quantities when the demand function intersects the input axis as given in Example 1 of Section 6.3 of Calculus Concepts: Suppose the demand for a certain model of minivan in the United States can be described as D(p) = 14.12(0.933.Chapter 6 The calculator draws the consumers’ surplus if you use the following method. − First, reset to have more room at the bottom of the Ymin graph.

Draw the graph of D. Then, with the graph on the screen, press At the TRACE (CALC) 7 ∫f(x)dx.TI-83, TI-83 Plus, TI-84 Plus Guide We add the demand function for the gasoline example used on page A-87 of this guide to calculate producers’ willingness and ability to receive. The demand and supply functions for the gasoline example in the text are given by D(p) = 5.43(0.607 million gallons and S(p) = 0 million gallons for p.

Programs for Various Calculators: and for Various CalculatorsHewlett Packard HP 38G:Please note: The first time each program function is exercised on the HP 38G, before executing the code, the calculator first takes a modest amount of time to compile it. As a consequence, all subsequent uses of that particular program function will run immediately and also much more quickly than they otherwise would. The latter two programs given below contain several different components, each of which must be compiled separately before running the first time.