Explanation Formula used: Theorem 2.1: Assume f is defined for all x near a except possibly at a . Then lim x → a f ( x ) = L if and only if lim x → a + f ( x ) = L and lim x → a − f ( x ) = L . The calculation the value of lim h → 0 ln ( 1 + h ) h is as follows. Substitute x = a in f ( h ) , f ( a ) = ln ( 1 + a ) a Substitute a = − 0.01 , − 0.001 , and -0 .0001 in f ( a ) = ln ( 1 + a ) a and find the left hand limit of f ( h ) = ln ( 1 + h ) h . Substitute a = − 0.01 in f ( a ) = ln ( 1 + a ) a , f ( − 0.01 ) = ln ( 1 − 0.01 ) − 0.01 = 1.00503 Substitute a = − 0.001 in f ( a ) = ln ( 1 + a ) a , f ( − 0.001 ) = ln ( 1 − 0.001 ) − 0.001 = 1.0005 Substitute a = − 0.0001 in f ( a ) = ln ( 1 + a ) a , f ( − 0.001 ) = ln ( 1 − 0.0001 ) − 0.0001 = 1.00005 Thus, the left hand limits are tabulated below: h −0.01 −0.001 −0.0001 f ( h ) = ln ( 1 + h ) h 1

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ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

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Chapter 2.2, Problem 35E

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To estimate: The value of limh→0ln(1+h)h by creating table of function values for h=0.01,0.001 , and 0.0001 , and h=−0.01,−0.001 , and −0.0001 .

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Chapter 2.2, Problem 34E

Chapter 2.2, Problem 36E

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To estimate: The value of lim h → 0 ln ( 1 + h ) h by creating table of function values for h = 0.01 , 0.001 , and 0.0001 , and h = − 0.01 , − 0.001 , and − 0.0001 .

Solution Summary: The author explains the formula used to estimate the value of undersethto 0mathrmlim

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To estimate: The value of limh→0ln(1+h)h by creating table of function values for h=0.01,0.001 , and 0.0001 , and h=−0.01,−0.001 , and −0.0001 .

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