Solution: Working with parametric equations Consider the

Chapter 8, Problem 10E

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QUESTION:

Consider the following parametric equations.

a. Make a brief table of values of t, x, and y.

b. Plot the points in the table and the full parametric curve, indicating the positive orientation (the direction of increasing t).

c. Eliminate the parameter to obtain an equation in x and y.

d. Describe the curve.

\(x=\ln 5t,\ y=\ln t^2;\ 1\ \leq\ t\ \leq\ e\)

Questions & Answers

QUESTION:

Consider the following parametric equations.

a. Make a brief table of values of t, x, and y.

b. Plot the points in the table and the full parametric curve, indicating the positive orientation (the direction of increasing t).

c. Eliminate the parameter to obtain an equation in x and y.

d. Describe the curve.

\(x=\ln 5t,\ y=\ln t^2;\ 1\ \leq\ t\ \leq\ e\)

ANSWER:

SolutionStep 1: Table of the values of t, x and y:11.60901.21.7910.1821.41.9460.3361.62.0790.471.82.190.58722.300.6932.22.3970.7882.42.4840.8752.62.5640.955e2.6091

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