(d) As h → 0, what is the limiting value of your result to part (c)? (e) What is its physical meaning of your result to part (d) if again x represents time and y represents the displacement?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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Please help me answer part (d) and part (e) only.

The answer of (a) : 25, 50

The answer of (b) : rate of change in the displacement of the particle

The answer of (c) : 100 - h

2. Consider the function y(x) = 5x over the interval [0, 10].
(a) If the points A(0, y(0)), B(5, y(5)), and C(10, y(10)) are on the curve
represented by the above function, find the slope of the lines (secants) AB, and AC, respectively.
(b) If x represents time and y represents the displacement of a particle moving along
a line, what is the physical meaning of your results to part (a)?
(c) Now consider a point D(10 – h, y(10 – h)) on the curve represented by the
given function, find the slope of the line DC.
(d) As h → 0, what is the limiting value of your result to part (c)?
(e) What is its physical meaning of your result to part (d) if again x represents time
and y represents the displacement?
Transcribed Image Text:2. Consider the function y(x) = 5x over the interval [0, 10]. (a) If the points A(0, y(0)), B(5, y(5)), and C(10, y(10)) are on the curve represented by the above function, find the slope of the lines (secants) AB, and AC, respectively. (b) If x represents time and y represents the displacement of a particle moving along a line, what is the physical meaning of your results to part (a)? (c) Now consider a point D(10 – h, y(10 – h)) on the curve represented by the given function, find the slope of the line DC. (d) As h → 0, what is the limiting value of your result to part (c)? (e) What is its physical meaning of your result to part (d) if again x represents time and y represents the displacement?
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