Explanation Given: Two formulas are: If k ≠ 0 then ∫ e k x d x = 1 k e k x + C and, If b > 0 and b ≠ 1 then ∫ b x d x = 1 ln b b x + C Calculation: First part is, If k ≠ 0 then ∫ e k x d x = 1 k e k x + C 1 k e k x is the anti-derivative of the function. So, if the differentiation of becomes 1 k e k x function e k x then this will prove the theorem

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 4.4, Problem 73P

To determine

To prove: use differentiation to prove two formulas.

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Chapter 4.4, Problem 72P

Chapter 4.4, Problem 74P

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