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# Explain why or why not Determine whether the | Ch 10 - 1RE

ISBN: 9780321570567 2

## Solution for problem 1RE Chapter 10

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition

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Problem 1RE

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

a. A set of parametric equations for a given curve is always unique.

b. The equations $$x=e^{t}$$, $$y=2 e^{t}$$ for $$-\infty<t<\infty$$ describe a line passing through the origin with slope 2 .

c. The polar coordinates $$(3,-3 \pi / 4)$$ and $$(-3, \pi / 4)$$ describe the same point in the plane.

d. The limaçon $$r=f(\theta)=1-4 \cos \theta$$ has an outer and inner loop. The area of the region between the two loops is $$\frac{1}{2} \int_{0}^{2 \pi}(f(\theta))^{2} d \theta$$.

e. The hyperbola $$y^{2} / 2-x^{2} / 4=1$$ has no x-intercepts.

f. The equation $$x^{2}+4 y^{2}-2 x=3$$ describes an ellipse.

Step-by-Step Solution:

Solution 1REStep 1:(a).A set of parametric equations for a given curve is always unique.This statement is false.A curve in the plain is said to be parameterized if the set of coordinates on the curve (x,y) are represented as a function of variable t.Namely , where D is a set of real numbers.The variable t is called a parameter and the relations between x,y and t are called the parametric equations.The D is called the domain of f and g and it is the set of values t takes.Let us consider an example .Consider a parabola Here if we take If we take ie and are parametric equations for the parabola .Thus a set of parametric equations for a given curve is not always unique.

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##### ISBN: 9780321570567

The full step-by-step solution to problem: 1RE from chapter: 10 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 1RE from 10 chapter was answered, more than 371 students have viewed the full step-by-step answer. The answer to “?Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.a. A set of parametric equations for a given curve is always unique.b. The equations $$x=e^{t}$$, $$y=2 e^{t}$$ for $$-\infty<t<\infty$$ describe a line passing through the origin with slope 2 .c. The polar coordinates $$(3,-3 \pi / 4)$$ and $$(-3, \pi / 4)$$ describe the same point in the plane.d. The limaçon $$r=f(\theta)=1-4 \cos \theta$$ has an outer and inner loop. The area of the region between the two loops is $$\frac{1}{2} \int_{0}^{2 \pi}(f(\theta))^{2} d \theta$$.e. The hyperbola $$y^{2} / 2-x^{2} / 4=1$$ has no x-intercepts.f. The equation $$x^{2}+4 y^{2}-2 x=3$$ describes an ellipse.” is broken down into a number of easy to follow steps, and 111 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: describe, equations, intercepts, cos, Counterexample. This expansive textbook survival guide covers 112 chapters, and 7700 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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Explain why or why not Determine whether the | Ch 10 - 1RE