Explanation Given information: The expression, lim x → 0 ( x 2 cos 20 π x ) . Formula used: Squeeze Theorem states, consider three functions l ( x ) , m ( x ) and n ( x ) which satisfy the relation l ( x ) ≤ m ( x ) ≤ n ( x ) . If lim x → c l ( x ) = A and lim x → c n ( x ) = A then lim x → c m ( x ) = A , that is m ( x ) is squeezed between l ( x ) and n ( x ) and its limit is same as the two functions near that point. Calculation: Consider the expression, lim x → 0 ( x 2 cos 20 π x ) . Recall that range of cosine function lies between the interval [ − 1 , 1 ] that is mathematically, − 1 ≤ cos x ≤ 1 Or, − 1 ≤ cos ( 20 π x ) ≤ 1 Multiply the above equation by x 2 , − x 2 ≤ x 2 cos ( 20 π x ) ≤ x 2 Compare the above equation with Squeeze Theorem which states, consider three functions l ( x ) , m ( x ) and n ( x ) which satisfy the relation l ( x ) ≤ m ( x ) ≤ n ( x )

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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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 2.4, Problem 27E

To determine

To prove: The value of the expression limx→0(x2cos20πx)=0 using Squeeze Theorem and plot the graphs of f(x)=−x2 , g(x)=x2cos(20πx) and h(x)=x2 on the same screen to illustrate the result.

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Chapter 2.4, Problem 26E

Chapter 2.4, Problem 28E

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Chapter 2 Solutions

Biocalculus: Calculus For Life Sciences

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To prove: The value of the expression lim x → 0 ( x 2 cos 20 π x ) = 0 using Squeeze Theorem and plot the graphs of f ( x ) = − x 2 , g ( x ) = x 2 cos ( 20 π x ) and h ( x ) = x 2 on the same screen to illustrate the result.

Solution Summary: The author illustrates the value of the expression undersetxto 0mathrmlimleft using Squeeze Theorem.

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To prove: The value of the expression limx→0(x2cos20πx)=0 using Squeeze Theorem and plot the graphs of f(x)=−x2 , g(x)=x2cos(20πx) and h(x)=x2 on the same screen to illustrate the result.

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Chapter 2 Solutions