Explanation - For finding the equation y = f ( x ) , we have to solve both parametric equations and have to eliminate the variable t . (a) Derivative of a function in parametric form can be found by differentiating both functions with respect to the parametric variable and then by dividing them d y d x = d y d t d x d t = y ' ( t ) x ' ( t ) (b) After finding the equation , we have to differentiate the equation with respect to x, and have to find f ' ( x ) . Given:- c ( t ) = ( 2 t + 1 , 1 − 9 t ) i.e. x = 2 t + 1 , y = 1 − 9 t Formula Used:- (1) Differentiation of x n is d ( x n ) d x = n x n − 1 (2) d y d x = d y d t d x d t = y ' ( t ) x ' ( t ) (3) d C d x = 0 : C = Constant Calculation:- For finding f ( x ) , use x = 2 t + 1 , y = 1 − 9 t . x = 2 t + 1 t = x − 1 2 Putting the value of t , in y ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

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Question

Chapter 12.1, Problem 59E

To determine

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Find an equation $y = f (x)$ for the parametric curve and compute $\frac{d y}{d x}$ in two ways for

$c (t) = (2 t + 1, 1 - 9 t)$

(a) Using $\frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}} = \frac{y' (t)}{x' (t)}$ .

(b) By differentiation of $f (x)$ .

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Chapter 12.1, Problem 58E

Chapter 12.1, Problem 60E

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Chapter 12 Solutions

CALCULUS (CLOTH)

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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- Find an equation y = f ( x ) for the parametric curve and compute d y d x in two ways for c ( t ) = ( 2 t + 1 , 1 − 9 t ) (a) Using d y d x = d y d t d x d t = y ' ( t ) x ' ( t ) . (b) By differentiation of f ( x ) .

Solution Summary: The author explains how to find the equation y = f ( x) by solving both parametric equations and eliminating the variable t.

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Videos

-

Find an equation $y = f (x)$ for the parametric curve and compute $\frac{d y}{d x}$ in two ways for

$c (t) = (2 t + 1, 1 - 9 t)$

(a) Using $\frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}} = \frac{y' (t)}{x' (t)}$ .

(b) By differentiation of $f (x)$ .

Want to see the full answer?

Chapter 12 Solutions

- Find an equation y = f ( x ) for the parametric curve and compute d y d x in two ways for c ( t ) = ( 2 t + 1 , 1 − 9 t ) (a) Using d y d x = d y d t d x d t = y ' ( t ) x ' ( t ) . (b) By differentiation of f ( x ) .

Solution Summary: The author explains how to find the equation y = f ( x) by solving both parametric equations and eliminating the variable t.

Concept explainers

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- Find an equation y=f(x) for the parametric curve and compute dydx in two ways for c(t)=(2t+1,1−9t) (a) Using dydx=dydtdxdt=y'(t)x'(t). (b) By differentiation of f(x).

Want to see the full answer?

Chapter 12 Solutions

-

Find an equation $y = f (x)$ for the parametric curve and compute $\frac{d y}{d x}$ in two ways for

$c (t) = (2 t + 1, 1 - 9 t)$

(a) Using $\frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}} = \frac{y' (t)}{x' (t)}$ .

(b) By differentiation of $f (x)$ .