Explanation Given: lim x → 0 3 sin x + cos x − 1 4 x Formula used: lim x → c [ f ( x ) + g ( x ) ] = lim x → c f ( x ) + lim x → c g ( x ) Calculation: lim x → 0 3 sin x + cos x − 1 4 x , Now we have to simplify it, 3 sin x + cos x − 1 4 x = 3 sin x 4 x + cos x − 1 4 x

10th Edition

ISBN: 9780321979070

Author: Michael Sullivan

Publisher: PEARSON

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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 14.2, Problem 55AYU

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To find: The limit $\lim_{x \to 0} \frac{3 sin x + \cos x - 1}{4 x}$ , use the properties of limits and facts that $\lim_{x \to 0} \frac{\sin x}{x} = 1$ , $\lim_{x \to 0} \frac{cos x - 1}{x} = 0$ ; $\lim_{x \to 0} \sin x = 0$ ; $\lim_{x \to 0} \cos x = 1$ .

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Chapter 14.2, Problem 54AYU

Chapter 14.2, Problem 56AYU

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The limit lim x → 0 3 sin x + cos x − 1 4 x , use the properties of limits and facts that lim x → 0 sin x x = 1 , lim x → 0 cos x − 1 x = 0 ; lim x → 0 sin x = 0 ; lim x → 0 cos x = 1 .

Solution Summary: The author explains the formula used to find the limit lim x 0 3 sin

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To find: The limit $\lim_{x \to 0} \frac{3 sin x + \cos x - 1}{4 x}$ , use the properties of limits and facts that $\lim_{x \to 0} \frac{\sin x}{x} = 1$ , $\lim_{x \to 0} \frac{cos x - 1}{x} = 0$ ; $\lim_{x \to 0} \sin x = 0$ ; $\lim_{x \to 0} \cos x = 1$ .

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Chapter 14 Solutions

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The limit lim x → 0 3 sin x + cos x − 1 4 x , use the properties of limits and facts that lim x → 0 sin x x = 1 , lim x → 0 cos x − 1 x = 0 ; lim x → 0 sin x = 0 ; lim x → 0 cos x = 1 .

Solution Summary: The author explains the formula used to find the limit lim x 0 3 sin

Concept explainers

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To find: The limit lim x → 0 3sinx + cosx − 1 4x , use the properties of limits and facts that lim x → 0 sinx x = 1 , lim x → 0 cosx − 1 x = 0 ; lim x → 0 sinx = 0 ; lim x → 0 cosx = 1 .

Want to see the full answer?

Chapter 14 Solutions

Additional Math Textbook Solutions

To find: The limit $\lim_{x \to 0} \frac{3 sin x + \cos x - 1}{4 x}$ , use the properties of limits and facts that $\lim_{x \to 0} \frac{\sin x}{x} = 1$ , $\lim_{x \to 0} \frac{cos x - 1}{x} = 0$ ; $\lim_{x \to 0} \sin x = 0$ ; $\lim_{x \to 0} \cos x = 1$ .