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 3.3, Problem 19E
To determine

Find the equation of the tangent line usinggiven data.

Expert Solution

Answer to Problem 19E

The equation of the tangent line is y=23x2(π31) .

Explanation of Solution

Given:

The given curve is y=secx andthegiven point is (π3,2) .

Calculation:

Find the derivative of the function.

  y=secx

  dydx=secxtanx

Substitute the value of x=π3 in the derivative.

  dydx=sec(π3)tan(π3)=23=23

Slope =23

Use point-slope form for the equation of tangent line.

  yy1=m(xx1)y1=2,x1=π3,m=23y2=23(xπ3)y2+2=23x2π3+2y=23x2(π31)

Hence theequation of the tangent line is y=23x2(π31) .

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