Explanation Proof: The given equation is, lim x → 0 ln ( x + 1 ) x = 1 . Definition of derivative is, f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h . Use the above definition to solve the given function. f ′ ( x ) = lim h → 0 ln ( x + h ) − ln ( x ) h = lim h → 0 ln ( x + h x ) h = lim h → 0 ln ( 1 + h x ) h ( ∵ ln a − ln b = ln a b ) = lim h → 0 ln ( 1 + h x ) 1 h ( ∵ a ln b = ln b a ) Substitute

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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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 5.5, Problem 100E

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To show: The value of the given function is limx→0ln(x+1)x is 1.

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Chapter 5.5, Problem 99E

Chapter 5.6, Problem 1CQ

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Chapter 5 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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The value of the given function is lim x → 0 ln ( x + 1 ) x is 1.

Solution Summary: The author explains that the value of the given function is undersetxto 0mathrmlim

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Chapter 5 Solutions