Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 604: 55


The answer is $\frac{\text{dy}}{\text{dx}}=-\frac{9}{2}$.

Work Step by Step

First way: Using Eq. (8) we have $\frac{\text{dy}}{\text{dx}}=\frac{y'(t)}{x'(t)}=-\frac{9}{2}$. Second way: Since $x=2t+1$, so $t=(x-1)/2$. Substituting $t$ into $y=1-9t$ gives $y=1-9 (x - 1)/2$, $y=f(x)=-(9/2)x+11/2$. Differentiating $f(x)$ we get $\frac{\text{dy}}{\text{dx}}=-\frac{9}{2}$.
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