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 79E
To determine

Find the equation of the tangent line usinggiven data.

Expert Solution

Answer to Problem 79E

The equation of the tangent line is y=x .

Explanation of Solution

Given:

The given curves are x=t4+1 and y=t3+t . The parametric value is t=1 .

Calculation:

Find the x and y value at t=1 .

  x=t4+1=(1)4+1=2

  y=t3+t=(1)3+(1)=2

Find the slope.

Apply formula dydx=dydtdxdt .

  dydt=ddt(t3+t)

Apply sum rule (f+g)'=f'+g' .

  dydt=ddt(t3)+ddt(t)

Use derivative rule ddx(xn)=nxn1 .

  dydt=3t2+1

  dxdt=ddt(t4+1)

Apply sum rule (f+g)'=f'+g' .

  dxdt=ddt(t4)+ddt(1)

Use derivative rule ddx(xn)=nxn1 .

  dxdt=4t3

  dydx(slope)=3t2+14t3

At the value t=1 .

  dydx(slope)=3(1)2+14(1)3=44=1

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

  yy1=m(xx1)y1=2,x1=2,m=1y(2)=1(x2)y+2=x+2y+22=x+22y=x

Hence theequation of the tangent line is y=x .

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