(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?
(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?
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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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32fa5d6c-9c5b-4d1e-8766-3fabf2e02b29%2F25c81de2-8fa4-4427-bf4f-97a6df92ab6b%2Fz8vfpbg_processed.jpeg&w=3840&q=75)
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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