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 20E
To determine

Find the equation of the tangent line usinggiven data.

Expert Solution

Answer to Problem 20E

The equation of the tangent line is y=x+1 .

Explanation of Solution

Given:

The given curve is y=excosx and the given pointis (0,1) .

Calculation:

Find the derivative of the function.

  y=excosx

Apply product rule.

  (fg)=f'g+fg'

  dydx=ddx(ex)cosx+exddx(cosx)

Use derivative rule ddx(ex)=ex and ddx(cosx)=sinx .

  dydx=excosx+ex(sinx)dydx=ex(cosxsinx)

Substitute the value of x=0 in the derivative.

  dydx=ex(cosxsinx)=e0[cos(0)sin(0)]=1[10]=1

Slope =1

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

  yy1=m(xx1)y1=1,x1=0,m=1y1=1(x0)y1=xy1+1=x+1y=x+1

Hence theequation of the tangent line is y=x+1 .

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