Explanation Given: f ( x ) = sin x 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 Special limit involving sine and cosine lim x → 0 sin x x = 1 , lim x → 0 cos x − 1 x = 0 Calculation: In order to evaluate the limit lim Δ x → 0 f ( x + Δ x ) − f ( x ) Δ x where, f ( x ) = sin x . Put function in the limit as lim Δ x → 0 f ( x + Δ x ) − f ( x ) Δ x = lim Δ x → 0 s i n ( x + Δ x ) − sin x Δ x</

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 52SP

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

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Chapter 2, Problem 51SP

Chapter 2, Problem 53SP

Chapter 2 Solutions

Calculus

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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY

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 undersetDelta xto 0mathrmlimf(x+

Concept explainers

Videos

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

Want to see the full answer?

Chapter 2 Solutions