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6) Assume that f(t) is continuous on [a, b] and that u = g(t) is continuously differentiable on [a, b], then a) True b) False r9(b) [ f(g(t)) g'(t) dt = [ f(u) du. g(a)

6) Assume that f(t) is continuous on [a, b] and that u = g(t) is continuously differentiable on [a, b], then a) True b) False r9(b) [ f(g(t)) g'(t) dt = [ f(u) du. g(a)

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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6) Assume that f(t) is continuous on [a, b] and that u = g(t) is continuously differentiable on [a, b], then a) True b) False = 0 and 7) Assume that f is continuous and strictly increasing on [0, 1] with f(0) f(1) = 1 with f f(t)dt = Assume that g is the inverse of f on [0, 1]. Then So g(t)dt = ³. a) True b) False 8) If G(x) = a) True b) False rg(b) [ f(g(t)) g' (t) dt = [ f(u) du. g(a) 2²+1 a) True b) False In(t) dt then G'(1) = 2e - In(4). 9) Let R be the region bounded by the graphs of f(x) = cos(x) and g(x) = sin(x) where ≤x≤. If T is the solid obtained by revolving the region R around the x-axis, then the volume of T is 7. 10) The solution to the integral equation f(x) = 3+2 2 * t f (t) dt is f(x) = 3e²²-1. a) True b) False
Transcribed Image Text:6) Assume that f(t) is continuous on [a, b] and that u = g(t) is continuously differentiable on [a, b], then a) True b) False = 0 and 7) Assume that f is continuous and strictly increasing on [0, 1] with f(0) f(1) = 1 with f f(t)dt = Assume that g is the inverse of f on [0, 1]. Then So g(t)dt = ³. a) True b) False 8) If G(x) = a) True b) False rg(b) [ f(g(t)) g' (t) dt = [ f(u) du. g(a) 2²+1 a) True b) False In(t) dt then G'(1) = 2e - In(4). 9) Let R be the region bounded by the graphs of f(x) = cos(x) and g(x) = sin(x) where ≤x≤. If T is the solid obtained by revolving the region R around the x-axis, then the volume of T is 7. 10) The solution to the integral equation f(x) = 3+2 2 * t f (t) dt is f(x) = 3e²²-1. a) True b) False
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