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Chapter 7: Q. 61 (page 592)

In Exercises 59鈥�62 use the derivative test in Theorem 7.6 to analyze the monotonicity of the given sequence.

sinkk

Short Answer

Expert verified

The test can't analyze the monotonicity of the given sequence.

Step by step solution

01

Step 1. Given Information.

The given sequence issinkk.

02

Step 2. Use the derivative test. 

To analyze the monotonicity of the given sequence we will use the derivative test.

Let the function is f(k)=sinkk.

According to the derivative test,

f'(k)=kcosk-sinkk2f'(k)=kcosk-sinkk2

Now, the sign of f'(k)changes an infinite number of times for k>0.

Therefore, the test can't analyze the monotonicity of the given sequence.

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