   Chapter 10.2, Problem 8E

Chapter
Section
Textbook Problem

# Find an equation of the tangent to the curve at the given point by two methods: (a) without eliminating the parameter and (b) by first eliminating the parameter.8. x = 1 + t ,   y = e t 2 ; (2, e)

(a)

To determine

To find: The equation of the tangent without eliminating the parameter for the parametric equations x=1+t and y=et2 .

Explanation

Given:

The parametric equation for the variable x is as follows.

x=1+t (1)

The parametric equation for the variable y is as follows.

y=et2 (2)

Calculation:

Differentiate the parametric equation (1) for x with respect to t .

x=1+tdxdt=12t

Differentiate the parametric equation (2) for y with respect to t .

y=et2dydt=et22t

Write the chain rule for dydx .

dydx=dydtdxdt

Substitute (et22t) for dydt and (12t) for dxdt in the above equation.

dydx=(et22t)[12t]=4t3/2et2 (3)

Write the equation for tangent

(b)

To determine

To find: The equation of the tangent by first eliminating the parameter for the parametric equations x=1+t and y=et2 .

### 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

#### Find more solutions based on key concepts 