Explanation Given information: The tangent of curve and point is 3 x 2 2 y and 1 , 1 . Graph: Consider the given tangent of curve equation, d y d x = 3 x 2 2 y Apply the separation of variables method and simplify. 2 y d y = 3 x 2 d x Integrate the both side of the equation and find the solution, ∫ 2 y d y = − ∫ 3 x 2 d x 2 y 2 2 = 3 x 3 3 + c y 2 = x 3 + c Where, c is an arbitrary constant

Calculus: Early Transcendentals, Enhanced Etext

12th Edition

ISBN: 9781119777984

Author: Howard Anton; Irl C. Bivens; Stephen Davis

Publisher: Wiley Global Education US

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Chapter 8.2, Problem 28ES

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To graph: The curve, which tangent is 3x22y and passing through the point 1,1 .

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Chapter 8.2, Problem 27ES

Chapter 8.2, Problem 29ES

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(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Pro

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Chapter 8 Solutions

Calculus: Early Transcendentals, Enhanced Etext

Ch. 8.1 - Match each differential equation with its family...Ch. 8.1 - If y=C1e2x+C2xe2x is the general solution of a...Ch. 8.1 - The graph of a differentiable function y=yx passes...Ch. 8.1 - A glass of ice water with a temperature of 36F is...Ch. 8.1 - Confirm that y=3ex3 is a solution of the...Ch. 8.1 - Confirm that y=14x4+2cosx+1 is a solution of the...Ch. 8.1 - State the order of the differential equation, and...Ch. 8.1 - Prob. 4ES Ch. 8.1 - Determine whether the statement is true or false....Ch. 8.1 - Determine whether the statement is true or false....

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To graph: The curve, which tangent is 3 x 2 2 y and passing through the point 1 , 1 .

Solution Summary: The author explains how to graph the tangent of the curve, which passes through the point (1,1).

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To graph: The curve, which tangent is 3x22y and passing through the point 1,1 .

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Chapter 8 Solutions