Explanation Given information: f ( θ ) = sin θ − θ θ 3 . Calculations: The value of the limit lim θ → 0 f ( θ ) is determined by putting several value of θ Now, lim θ → 0 f ( θ ) = lim θ → 0 sin θ − θ θ 3 When θ = + 0.002 then the value of f ( θ ) is f ( θ ) = sin θ − θ θ 3 f ( 0.002 ) = sin 0.002 − 0.002 0.002 3 = − 0.167 When θ = − 0.002 then the value of f ( θ ) is f ( θ ) = sin θ − θ θ 3 f ( − 0.002 ) = sin ( − 0.002 ) − 0.002 − 0.002 3 f ( 0.002 ) = sin 0.002 − 0.002 − 0.002 3 = 0.167 When θ = + 0.0001 then the value of f ( θ ) is f ( θ ) = sin θ − θ θ 3 f ( 0.0001 ) = sin 0.0001 − 0.0001 0.0001 3 = − 0.167 When θ = − 0.0001 then the value of f ( θ ) is f ( θ ) = sin θ − θ θ 3 f ( − 0

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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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 2.2, Problem 4E

To determine

The value of the limit.

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Chapter 2.2, Problem 3E

Chapter 2.2, Problem 5E

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Name: Knowledge and Understanding Use the sketch of f(x) for questions 1, 2 & 3. 1. List the places where f(x) is not differentiable. 2. Where is f(x) not differentiable because f(x) is vertical? 3. For each section place the corresponding letter on the blank. A) 0 D) Does Not Exist a) f(1) b) f'(3) ____c) f'(-0.5)_ _d) f"(1)_ It 3 2 +

2. Determine whether these are well-defined functions. Explain. 3 (a) f:R → R, where f(x) = x² + 5° 7 (b) g: (5, 0) → R, where g(x) = 4 (c) h:R → R, where h(x) = –/7 – 4x + 4x². |

Chapter 2 Solutions

CALCULUS (CLOTH)

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E

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The value of the limit.

Solution Summary: The author calculates the value of the limit by putting several values of theta .

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The value of the limit.

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Chapter 2 Solutions