3. (a) Show all functions satisfying u"(x) = 0 are linear by integrating the expression of u"(x) %3D twice with respect to x. (b) Suppose one such function satisfies u(-1) = 0 and u(1) = 5. Determine the exact form of u(x).

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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help on homework question 3

1. Explain what is wrong with the following statement: "The right sum with 20 rectangles ap-
proximating the integral log x dx is
1
[log 2 + log 2.05 + log 2.10 +...+ log 2.95 + log 3]"
20
and explain how to correct the above equation to attain the correct approximation.
2. Suppose
f (x) dx = -5 and
f(x) dx = 6.
Compute
2f(x) + (3x – 4)² dx.
3. (a) Show all functions satisfying u" (x)
twice with respect to x.
= 0 are linear by integrating the expression of u"(x)
(b) Suppose one such function satisfies u(-1) = 0 and u(1) = 5. Determine the exact form of
u(x).
4. Compute the following:
(a) L.
e dx
d
(b)
dx
f' (x) dx
5. Given
x2
f (x) :
if x < 1
1
if x > 1,
f(æ) da.
evaluate
Transcribed Image Text:1. Explain what is wrong with the following statement: "The right sum with 20 rectangles ap- proximating the integral log x dx is 1 [log 2 + log 2.05 + log 2.10 +...+ log 2.95 + log 3]" 20 and explain how to correct the above equation to attain the correct approximation. 2. Suppose f (x) dx = -5 and f(x) dx = 6. Compute 2f(x) + (3x – 4)² dx. 3. (a) Show all functions satisfying u" (x) twice with respect to x. = 0 are linear by integrating the expression of u"(x) (b) Suppose one such function satisfies u(-1) = 0 and u(1) = 5. Determine the exact form of u(x). 4. Compute the following: (a) L. e dx d (b) dx f' (x) dx 5. Given x2 f (x) : if x < 1 1 if x > 1, f(æ) da. evaluate
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