315% D Tue 9:20 PM a Sana https://edugen.wileyplus.com/edugen/lt IS Hughes-Halle

Question

315% D Tue 9:20 PM a Sana https://edugen.wileyplus.com/edugen/lt IS Hughes-Hallett, Applied Calculus, Se Grace Period: 8 days left I Register N Chapter 1, Section 1.10, Question 011 Values of a function are given in the following table. Explain why this function appears to be Assuming that the function is periodic, estimate its value at 10, at70, and at 135 periodic. Approximately what are the period and amplitude of the function? ?120125130|35|40|45150|55160- f(? 1.8 | 1.4 | 1.7 | 2.3 | 2.0 | 1.8 | 1.4 | 1.7 | 2.3 Enter the exact answers. t- The function appears to be periodic because the table data begins to repeat itself at The period is The amplitude is f (10)- (70)

Explanation / Answer

Observe that the values of given function repeat themselves - and the pattern of values in one cycle is

{1.8, 1.4, 1.7, 2.3, 2.0}

and these values repeat themselves as t goes from 20 to 40 inclusive, at space interval of 5. So we have all the information now to answer as,

The function appears to be periodic because the table data begins to repeat itself at t = 45

Explanation - Note that f(20) = f(45) = 1.8

The period is 25

Explanation - Note that a period is the smallest interval T such that f(x+T) = f(x). Now we have f(20) = f(45). So clearly, the period is 45-20 = 25

The amplitude is 0.45

Explanation - Amplitude is defined as half the difference between maximum and minimum values of the function. Here f(t)min = 1.4 and f(t)max = 2.3. So ampitude is half of (2.3 – 1.4) viz. 0.45

f(10) = f(35) = 2.3

f(70) = f(20) = 1.8

f(135) = f(35) = 2.3

Explanation - Recall that f(x) = f(x+T). In obtaining above values, we have made use of this property. So for f(10) we added one time period viz. 25, and so it equals f(35) Similarly for f(70) we subtracted two time periods viz. 70 – 50 so it equals f(20). Note that we can both add or subtract time periods.

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