   Chapter 10.3, Problem 92E

Chapter
Section
Textbook Problem

# Using Parametric Equations Use the parametric equations x = t 2 3     and     y = 3 t − 1 3 t 5 to answer the following.Use a graphing utility to graph the curve on the interval − 3 ≤ t ≤ 3 .(b) Find d y / d x and d 2 y / d x 2 . (c) Find the equation of the tangent line at the point ( 3 , 8 3 ) .(d) Find the length of the curve on the interval − 3 ≤ t ≤ 3 .(e) Find the area of the surface generated by revolving the curve about the x-axis.

a)

To determine

Graph the curve by the use of graphing utility on the interval 3t3

Explanation

a) Given: x=t23 and y=3tt33

b) Calculation:

Graph the curve on the interval 3t3

Steps to draw the graph using graphing utility:

Step1: Press ON key

b)

To determine
dydx and d2ydx2

c)

To determine
The equation of tangent line at the point (3,83)

d)

To determine
Length of curve on the interval 3t3.

e)

To determine
The area of surface generated by revolving the curve about x axis.

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