Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Sum and constant-multiple rules: State the sum and constant-multiple rules for (a) derivatives and (b) limits.

(a) The sum rule for derivatives states that the derivative of a sum is equal to the sum of the derivatives.

Sum rule of derivatives:

$\frac{d}{d x} [f (x) + g (x)] = \frac{d}{d x} f (x) + \frac{d}{d x} g (x)$

The Constant multiple rule says the derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function.

Constant multiple rule:

$\frac{d}{d x} [k \cdot f (x)] = k \cdot \frac{d}{d x} f (x)$

(b) Sum law for limits states that the limit of the sum of two functions equals to the sum of the limits of two functions.

Sum rule of limit:

$\lim_{x \to c} [f (x) + g (x)] = \lim_{x \to c} f (x) + \lim_{x \to c} g (x)$

Constant multiple law for limits states that the limit of a constant multiple of a function equals the product of the constant with the limit of the function.

Constant multiple of limit:

$\lim_{x \to c} [k \cdot f (x)] = k \cdot \lim_{x \to c} f (x)$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information:

We want to State the sum and constant-multiple rules for

(a) derivatives
(b) limits.

Part (a) Step 1. Solution of (a):

The sum rule for derivatives states that the derivative of a sum is equal to the sum of the derivatives.

Sum rule:

$\frac{d}{d x} [f (x) + g (x)] = \frac{d}{d x} f (x) + \frac{d}{d x} g (x)$

The Constant multiple rule says the derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function.

Constant multiple rule:

$\frac{d}{d x} [k \cdot f (x)] = k \cdot \frac{d}{d x} f (x)$

Part (b) Step 1. Solution:

Sum law for limits states that the limit of the sum of two functions equals to the sum of the limits of two functions.

Sum Law:

$\frac{d}{d x} [f (x) + g (x)] = \frac{d}{d x} f (x) + \frac{d}{d x} g (x)$

Constant multiple law for limits states that the limit of a constant multiple of a function equals the product of the constant with the limit of the function.

Constant multiple law:

$\lim_{x \to c} [k \cdot f (x)] = k \cdot \lim_{x \to c} f (x)$

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Calculus

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Short Answer

Sum and constant-multiple rules: State the sum and constant-multiple rules for (a) derivatives and (b) limits.

Step by Step Solution

Step 1. Given Information:

Part (a) Step 1. Solution of (a):

Part (b) Step 1. Solution:

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Calculus

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Short Answer

Sum and constant-multiple rules: State the sum and constant-multiple rules for (a) derivatives and (b) limits.

Step by Step Solution

Step 1. Given Information:

Part (a) Step 1. Solution of (a):

Part (b) Step 1. Solution:

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