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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

3. x = t3 + l, y = t 4 + t; t = −1

To determine

To find: The equation of the tangent for the parametric equations x=t3+1 and y=t4+t.

Explanation

Given:

The parametric equation for the variable x is as follows.

x=t3+1 (1)

The parametric equation for the variable y is as follows.

y=t4+t (2)

Calculation:

Differentiate the parametric equation x with respect to t.

x=t3+tdxdt=3t2

Differentiate the parametric equation y with respect to t.

y=t4+tdydt=4t3+1

Write the chain rule for dydx.

dydx=dydtdxdt=(4t3+1)(3t2)=4t3+13t2 (3)

Substitute for (4t3+1) for dydt and (3t2) for dxdt in the above equation.

Write the equation for tangent

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