Explanation Given: f ( x ) = x ( x + 1 ) Concept Used: Constant rule for limits: lim x → c k = k for any constant k To find lim Δ x → 0 f ( x + Δ x ) − f ( x ) Δ x put function in this limit and evaluate Calculation: In order to evaluate the limit lim Δ x → 0 f ( x + Δ x ) − f ( x ) Δ x Where, f ( x ) = x ( x + 1 ) Put function in the limit as lim Δ x → 0 f ( x + Δ x ) − f ( x ) Δ x = lim Δ x → 0 ( x + Δ x ) ( x + Δ x + 1 ) − x ( x + 1 ) Δ x = lim Δ x → 0 ( x ) ( x + Δ x + 1

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 2, Problem 50SP

To determine

To evaluate the limit limΔx→0f(x+Δx)−f(x)Δxfor given f(x) .

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Chapter 2, Problem 49SP

Chapter 2, Problem 51SP

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Chapter 2 Solutions

Calculus

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To evaluate the limit lim Δ x → 0 f ( x + Δ x ) − f ( x ) Δ x for given f ( x ) .

Solution Summary: The author explains how to evaluate the limit undersetxto 0mathrmlimf(x+Delta x

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To evaluate the limit limΔx→0f(x+Δx)−f(x)Δxfor given f(x) .

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Chapter 2 Solutions