Let f : [0, π] → R be defined byf (x) =(0 if x = 0,x sin 1x − 1x cos 1x if x̸ = 0.Is f continuous?

Question

Let f : [0, π] → R be defined byf (x) =(0 if x = 0,x sin 1x − 1x cos 1x if x̸ = 0.Is f continuous?
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Solution 1

To determine if the function f is continuous, we need to check if the limit of the function as x approaches 0 is equal to the value of the function at x=0.

The function is defined differently for x=0 and x≠0, so we need to consider these cases separately.

For x=0, the function is defined as f(x) Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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