CalculusVolume2-SASG-07-02

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OpenStax Calculus Volume 2 Student Answer and Solution Guide Chapter 7 Parametric Equations and Polar Coordinates 7.2 Calculus of Parametric Curves Section Exercises For the following exercises, each set of parametric equations represents a line. Without eliminating the parameter, find the slope of each line. 63. Answer: 0 65. Answer: For the following exercises, determine the slope of the tangent line, then find the equation of the tangent line at the given value of the parameter. 67. Answer: 69. Answer: Slope is undefined; For the following exercises, find all points on the curve that have the given slope. 71. slope = 0.5 Answer: 73. Answer: No points possible; undefined expression.

OpenStax Calculus Volume 2 Student Answer and Solution Guide

OpenStax Calculus Volume 2 Student Answer and Solution Guide For the following exercises, write the equation of the tangent line in Cartesian coordinates for the given parameter t . 75. Answer: 77. Answer: 79. For where Find all values of t at which a vertical tangent line exists. Answer: 81. Find for Answer: 83. For the curve find the slope and concavity of the curve at Answer: and so the curve is neither concave up nor concave down at Therefore, the graph is linear and has a constant slope but no concavity. 85. Find the slope and concavity for the curve whose equation is at Answer: the curve is concave down at 87. Find all points on the curve at which horizontal and vertical tangents exist. Answer: No horizontal tangents. Vertical tangents at

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