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 3.4, Problem 44E
To determine

Find the equation of the tangent line for the given curve.

Expert Solution

Answer to Problem 44E

The equation of the tangent line is y=x .

Explanation of Solution

Given:

The given curve is y=sinx+sin2x and the given point is (0,0) .

Calculation:

Find the slope of the tangent line at the given point (0,0) .

Find first derivative of the given equation y=sinx+sin2x .

Use sum rule.

  (f+g)'=f'+g'

  y'=ddx(sinx)+ddx(sin2x)

Apply chain rule.

  df(a)dx=dfdadadx

Let f=a2,a=sinx

  y'=ddx(sinx)+dda(a2)ddx(sinx)

Use derivative rule ddx(sinx)=cosx and ddx(xn)=nxn1 .

  y'=cosx+2acosx

Substitute the value of a=sinx .

  y'=cosx+2sinxcosxy'=cosx(1+2sinx)

Plug in the x=0 into the derivative.

  y'=cos(0)(1+2sin(0))=1(1+20)=1

Slope of the tangent line is 1 .

Use point-slope form of the equation (For the equation of tangent line).

  yy1=m(xx1)y1=0,x1=0,m=1y0=1(x0)y=x

Hence theequation of the tangent line is y=x .

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