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ons, use your work (a) to help you the generar (Recall that general antiderivative of a function includes "+C" to reflect the entire family of functions that share the same derivative.) Notice the label of antiderivative respects the name (e.g., the antiderivative of m should be called M). In addition, check your work by computing the derivative each proposed antiderivative. (i) If m(x) = e³, then M(x) = = (ii) If n(x) = cos(5x + 1), then (iii) If s(x) 1 1+4x2' (iv) If v(x) = (2-7x)³, then (v) If w(x) = 34-112, then then = = =

ons, use your work (a) to help you the generar (Recall that general antiderivative of a function includes "+C" to reflect the entire family of functions that share the same derivative.) Notice the label of antiderivative respects the name (e.g., the antiderivative of m should be called M). In addition, check your work by computing the derivative each proposed antiderivative. (i) If m(x) = e³, then M(x) = = (ii) If n(x) = cos(5x + 1), then (iii) If s(x) 1 1+4x2' (iv) If v(x) = (2-7x)³, then (v) If w(x) = 34-112, then then = = =

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.2: Polynomial Functions
Problem 96E: What is the purpose of the Intermediate Value Theorem?
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(b) For each of the following functions, use your work in (a) to help you determine the general antiderivative of the function. (Recall that the general antiderivative of a function includes ``+C" to reflect the entire family of functions that share the same derivative.) Notice the label of each antiderivative respects the name (e.g., the antiderivative of m should be called M). In addition, check your work by computing the derivative of each proposed antiderivative. (i) If m(x) = e³, then M(x) = (ii) If n(x) = cos(5x + 1), then 1 (iii) If s(x)= 1+ 4x² (iv) If v(x) = (2 – 7x)³, then (v) If w(x) = 34-11ª, then 9 then ←I = || || = FI →
Transcribed Image Text:(b) For each of the following functions, use your work in (a) to help you determine the general antiderivative of the function. (Recall that the general antiderivative of a function includes ``+C" to reflect the entire family of functions that share the same derivative.) Notice the label of each antiderivative respects the name (e.g., the antiderivative of m should be called M). In addition, check your work by computing the derivative of each proposed antiderivative. (i) If m(x) = e³, then M(x) = (ii) If n(x) = cos(5x + 1), then 1 (iii) If s(x)= 1+ 4x² (iv) If v(x) = (2 – 7x)³, then (v) If w(x) = 34-11ª, then 9 then ←I = || || = FI →
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