   Chapter 10.2, Problem 3E

Chapter
Section
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

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

31. Expand .

Mathematical Applications for the Management, Life, and Social Sciences

Change 1500 mL or L.

Elementary Technical Mathematics

Find the following products 6i(38i)

Trigonometry (MindTap Course List)

In Exercises 1-22, evaluate the given expression. P(5,3)

Finite Mathematics for the Managerial, Life, and Social Sciences

0 1 does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 