   Chapter 10.5, Problem 58E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 55-58, estimate the given quantity. f ( x ) = ln x ;  estimate  f ' ( 2 )

To determine

To calculate: The value of f(2) from the function f(x)=lnx.

Explanation

Given Information:

The provided function is f(x)=lnx.

Formula used:

The balanced difference quotient:

When f is differentiable at a, the approximate value of f'(a) can be calculated as,

f'(a)=f(a+h)f(ah)2h

Where, the value of h=0.0001.

Calculation:

Consider the function f(x)=lnx.

Now, apply the balanced difference quotient formula and substitute the value a=2 and h=0.0001:

f(2)=f(2+0.0001)f(20.0001)2(0.0001)

Calculate f(2+0.0001) by substituting 2+0.0001 in the function f(x)=lnx:

f(2+0

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