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?In Exercises 7-18, find and simplify the function values. \(f(x, y)=3 x^{2}-2 y\) (a) \(\frac{f(x+\Delta x, y)-f(x, y)}{\Delta x}\)

Calculus: Early Transcendental Functions | 6th Edition | ISBN: 9781285774770 | Authors: Ron Larson ISBN: 9781285774770 141

Solution for problem 18 Chapter 13.1

Calculus: Early Transcendental Functions | 6th Edition

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Calculus: Early Transcendental Functions | 6th Edition | ISBN: 9781285774770 | Authors: Ron Larson

Calculus: Early Transcendental Functions | 6th Edition

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Problem 18

In Exercises 7-18, find and simplify the function values.

\(f(x, y)=3 x^{2}-2 y\)

(a) \(\frac{f(x+\Delta x, y)-f(x, y)}{\Delta x}\)

(b) \(\frac{f(x, y+\Delta y)-f(x, y)}{\Delta y}\)

Text Transcription:

f(x, y) = 3x^2 - 2y

f(x + Delta x, y) - f(x, y) / Delta x

f(x, y + Delta y) - f(x, y) / Delta y

Step-by-Step Solution:

Step 1 of 5) converges. To see this, we ignore the first three terms and compare the remaining terms with those of the convergent geometric series gqn =0(1>2n). The term 1>12n + 2n2 of the truncated sequence is less than the corresponding term 1>2n of the geometric series. We see that term by term we have the comparison

Step 2 of 2

Chapter 13.1, Problem 18 is Solved
Textbook: Calculus: Early Transcendental Functions
Edition: 6
Author: Ron Larson
ISBN: 9781285774770

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?In Exercises 7-18, find and simplify the function values. \(f(x, y)=3 x^{2}-2 y\) (a) \(\frac{f(x+\Delta x, y)-f(x, y)}{\Delta x}\)