A function f is defined as follows \[f(x)={{x}^{p}}\cos \left( \frac{1}{x} \right),x\ne 0f(0)=0\] What conditions should be imposed on p so that f may be continuous at x = 0?

A function f is defined as follows \[f(x)={{x}^{p}}\cos \left( \frac{1

1.	A function f is defined as follows \[f(x)={{x}^{p}}\cos \left( \frac{1}{x} \right),x\ne 0f(0)=0\] What conditions should be imposed on p so that f may be continuous at x = 0?
A.	p = 0
B.	p > 0
C.	p < 0
D.	No value of p
Answer» C. p < 0

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A function f is defined as follows \[f(x)={{x}^{p}}\cos \left( \frac{1}{x} \right),x\ne 0f(0)=0\] What conditions should be imposed on p so that f may be continuous at x = 0?

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