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Two students are calculating the instantaneous rate of change of y= sin(x) at x = Student A claims the rate of change can be represented by 1/2, while student B insists it is more accurately reported as 0.499996. Who is correct, and why?

Two students are calculating the instantaneous rate of change of y= sin(x) at x = Student A claims the rate of change can be represented by 1/2, while student B insists it is more accurately reported as 0.499996. Who is correct, and why?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Two students are calculating the instantaneous rate of change of y= sin(x) at x = 3. Student A claims the rate of change can be represented by 1/2, while student B insists it is more accurately reported as 0.499996. Who is correct, and why?
Transcribed Image Text:Two students are calculating the instantaneous rate of change of y= sin(x) at x = 3. Student A claims the rate of change can be represented by 1/2, while student B insists it is more accurately reported as 0.499996. Who is correct, and why?
Expert Solution
Step 1

Given is the function y=sinx and the point is x=π3

The rate of change is represented by two students in two different values.

The objective is to select the correct answer.

 

The instantaneous rate of change is the change in the derivative value at a specific given point.

So the instantaneous rate of change of a function at a point will be equal to the value of the derivative of the function at that point.

The derivative of the trigonometric function sine is ddxsinx=cosx.

 

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