a. Explanation Given information: x 2 + y 2 = 6 y − 10 and d y d x exist. Calculation: Differentiate x 2 + y 2 = 6 y − 10 with respect to x. x 2 + y 2 = 6 y − 10 d d x ( x 2 + y 2 ) = d d x ( 6 y − 10 ) d d x ( x 2 ) + d d x ( y 2 ) = 6 d d x ( y ) − d d x ( 10 ) ( 2 x 2 − 1 ) + ( 2 y 2 − 1 ) d y d x = 6 d y d x − d d x ( 10 ) b. To determine To show that there are no real numbers x, y that satisfy the equation x 2 + y 2 = 6 y − 10 . c. To determine To conclude from the result found in part a in light of the observation in part b.

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Question

Chapter 3.6, Problem 42PS

To determine

To show that dydx=x3−y .

To determine

To show that there are no real numbers x, y that satisfy the equation

x2+y2=6y−10 .

To determine

To conclude from the result found in part a in light of the observation in part b.

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Chapter 3.6, Problem 41PS

Chapter 3.6, Problem 43PS

Chapter 3 Solutions

Calculus

Ch. 3.1 - Prob. 1PS Ch. 3.1 - Prob. 2PS Ch. 3.1 - Prob. 3PS Ch. 3.1 - Prob. 4PS Ch. 3.1 - Prob. 5PS Ch. 3.1 - Prob. 6PS Ch. 3.1 - Prob. 7PS Ch. 3.1 - Prob. 8PS Ch. 3.1 - Prob. 9PS Ch. 3.1 - Prob. 10PS

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10 - Roots of polynomials; Author: Technion;https://www.youtube.com/watch?v=88YUeigknNg;License: Standard YouTube License, CC-BY

To show that d y d x = x 3 − y .

Solution Summary: The author explains how to calculate x2+y 2=6y-10 with respect to x.

Concept explainers

Videos

To show that dydx=x3−y .

To show that there are no real numbers x, y that satisfy the equation

x2+y2=6y−10 .

To conclude from the result found in part a in light of the observation in part b.

Want to see the full answer?

Chapter 3 Solutions

To show that d y d x = x 3 − y .

Solution Summary: The author explains how to calculate x2+y 2=6y-10 with respect to x.

Concept explainers

Videos

To show that dydx=x3−y .

To show that there are no real numbers x, y that satisfy the equation x2+y2=6y−10 .

To conclude from the result found in part a in light of the observation in part b.

Want to see the full answer?

Chapter 3 Solutions

To show that there are no real numbers x, y that satisfy the equation

x2+y2=6y−10 .