Explanation Given information: The function is t ( θ ) = sin θ − cos θ . Calculation: Consider the function. t ( θ ) = sin θ − cos θ Hence, there are no vertical and horizontal asymptote. Differentiate the function. t ′ ( θ ) = sin θ + cos θ Hence, the function is increasing for all θ < 3 π 4 , θ > 7 π 4 and decreasing for 3 π 4 < θ < 7 π 4 . Differentiate above equation. t ″ ( θ ) = − sin θ + cos θ It is clear that t ″ ( θ ) > 0 → θ < π 4 , θ > 5 π 4 for x > 0

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 4.4, Problem 41PS

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To explain: The point where the graph of given function is rising, falling, the concavity, the point of inflection and vertical and horizontal asymptotes.

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Chapter 4.4, Problem 40PS

Chapter 4.4, Problem 42PS

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(1) For each of the following, parameterize a circle of radius 5 centered at the origin. Simplify your functions where appropriate. (a) Parameterize the circle counter-clockwise, starting and ending at (5,0). Your parameter t should go between 0 and 27 and go once around the circle. (b) Parameterize the circle clockwise, starting and ending at (-5,0). Your parameter t should go between 0 and 27 and go once around the circle. (2) Consider the parameterized curve given by x =t+ Int y = 2t3 + 3t? t> 0 (a) Find dy. Simplify your answer. (b) Find the equation of the tangent line to the curve at t = 1. (c) Find . Simplify your answer. 1

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Chapter 4 Solutions

Calculus

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The point where the graph of given function is rising, falling, the concavity, the point of inflection and vertical and horizontal asymptotes.

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Chapter 4 Solutions