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Derivatives Consider the following parametric
Chapter 8, Problem 49E(choose chapter or problem)
Consider the following parametric curves.
a. Determine dy/dx in terms of t and evaluate it at the given value of t.
b. Make a sketch of the curve showing the tangent line at the point corresponding to the given value of t.
x = t + 1/t, y = t - 1/t; t = 1
Questions & Answers
QUESTION:
Consider the following parametric curves.
a. Determine dy/dx in terms of t and evaluate it at the given value of t.
b. Make a sketch of the curve showing the tangent line at the point corresponding to the given value of t.
x = t + 1/t, y = t - 1/t; t = 1
ANSWER:Solution 49EStep 1:Given ; x = t + , and y = t -; t = 1. = , and = - = 4…………….(1) 1. In this problem we need to determine in terms of ‘t’ and evaluate it at the given value of t .We know that = Consider , x = t + Differentiate both sides with respect to ‘t’ we get , (x) = ( t + ) = 1 - , since = At t= 1 , then = = 0Consider , y = t -Differentiate both sides with respect to ‘t’ we get , (y) = ( t - ) = 1 + , since = At t = 1, then = = 2Therefore , slope = = = At t = 1 , slope = = =