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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

  1. (a) Eliminate the parameter to find a Cartesian equation of the curve.
  2. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

15. x = t2, y = ln t

(a)

To determine

To find: obtain a Cartesian equation of the curve by eliminating parameter t .

Explanation

Given data:

The parametric equation for the variable x is as follows.

x=t2 (1)

The parametric equation for the variable y is as follows.

y=ln t (2)

Calculation:

Solving parametric equation y to obtain value t .

y=ln t

t=ey

Substitute t=ey in the parametric equation x ,

x=t2x=(

(b)

To determine

To plot: The curve using the parametric equations. x=t2 and y=ln t .

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