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Question 8. (a) Complete the statement of FTC Part I: Fundamental Theorem of Calculus Part I states that if f is a function continuous on [a,b], and if a ≤ x ≤ b such that g(x) = f* f(t)dt then g is continuous on [a, b], g is differentiable on (a, b), and g'(x) = A consequence of this theorem is that when a and b are differentiable functions then d pb(x) 1 (1) f(t)dt = f(b(x))( dx a(x) )-f(a(x))( (b) Consider the function f(t) = cos² (cos(t)) defined on [0,]. Set g(x) = f cos² (cos(t))dt, where 0 ≤ x ≤. Then g is continuous on same interval as f 0 and g'(x) =

Question 8. (a) Complete the statement of FTC Part I: Fundamental Theorem of Calculus Part I states that if f is a function continuous on [a,b], and if a ≤ x ≤ b such that g(x) = f* f(t)dt then g is continuous on [a, b], g is differentiable on (a, b), and g'(x) = A consequence of this theorem is that when a and b are differentiable functions then d pb(x) 1 (1) f(t)dt = f(b(x))( dx a(x) )-f(a(x))( (b) Consider the function f(t) = cos² (cos(t)) defined on [0,]. Set g(x) = f cos² (cos(t))dt, where 0 ≤ x ≤. Then g is continuous on same interval as f 0 and g'(x) =

Calculus: Early Transcendentals
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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Question 8. (a) Complete the statement of FTC Part I: Fundamental Theorem of Calculus Part I states that if f is a function continuous on [a, b], and if a ≤ x ≤ b such that g(x) = f* f(t)}dt then g is continuous on [a, b], g is differentiable on (a, b), and g'(x) = A consequence of this theorem is that when a and b are differentiable functions then d = ( f(t)dt = f(b(x)) ( dx a(x) )-f(a(x))( (b) Consider the function f(t) = cos² (cos(t)) defined on [0,5]. Set g(x) = f cos² (cos(t))dt, where 0≤x≤. Then g is continuous on same interval as f 0 and g'(x)
Transcribed Image Text:Question 8. (a) Complete the statement of FTC Part I: Fundamental Theorem of Calculus Part I states that if f is a function continuous on [a, b], and if a ≤ x ≤ b such that g(x) = f* f(t)}dt then g is continuous on [a, b], g is differentiable on (a, b), and g'(x) = A consequence of this theorem is that when a and b are differentiable functions then d = ( f(t)dt = f(b(x)) ( dx a(x) )-f(a(x))( (b) Consider the function f(t) = cos² (cos(t)) defined on [0,5]. Set g(x) = f cos² (cos(t))dt, where 0≤x≤. Then g is continuous on same interval as f 0 and g'(x)
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