   Chapter 4.8, Problem 9E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Using a Tangent Line Approximation In Exercises 5-12, find the tangent line approximation T to the graph of f at the given point. Then complete the table. X 1.9 1.99 2 2.01 2.1 f(x) f(x) f ( x ) = sin x ,       ( 2 , sin 2 )

To determine

To calculate: The missing values in the table given below after obtaining the tangent line approximation T for the provided function f(x)=sinx.

x1.91.9922.012.1f(x)T(x)

Explanation

Given:

The function f(x)=sinx and the point (2,sin2).

The table,

x1.91.9922.012.1f(x)T(x)

Formula Used:

For the function f and a point (c,f(c)), the tangent line approximation is given by:

T(x)=f(c)+f'(c)(xc)

Calculation:

Differentiate the provided function,

f(x)=sinxf'(x)=cosx

Now calculate the derivative at 2

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