BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3, Problem 5P
To determine

To find: The value of f(π4).

Expert Solution

Answer to Problem 5P

The value of f(π4) is 32.

Explanation of Solution

Definition used:

The derivative of f(x) at a, f(a)=limh0f(x+h)f(x)h.

Calculation:

The function is f(x)=limtxsectsecxtx.

Replace t to x+h then h approaches to zero.

f(x)=limh0sec(x+h)secxx+hx=limh0sec(x+h)secxh=ddx(secx)=secxtanx

Obtain the derivative f(x)=secxtanx.

f(x)=ddx(f(x))=ddx(secxtanx)=secxddx(tanx)+tanxddx(secx)=secxsec2x+tanxsecxtanx

Substitute x=π4 in f(x),

f(π4)=sec(π4)sec2(π4)+tan(π4)sec(π4)tan(π4)=(2)(2)2+1(2)1=2(2)+2=32

Therefore, the value of f(π4) is 32.

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