For what value of k is the function

f(x)= tan5x sin2x , when x is not equal to zero

k , x=0

continuous at x=0?

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For what value of k is the function
f(x)= tan5x sin2x , when x is not equal to zero
k , x=0
continuous at x=0?

Ayush Jha · Accepted Answer

For any function f(x) to be continuous at x=0 $\lim_{x \to 0^{-}} f (x) = \lim_{x \to 0^{+}} f (x) = f (0)$ So, $\lim_{x \to 0} f (x) = \tan 5 (0) \sin 2 (0) = 0$ Therefore, k=0

For what value of k is the function f(x)= tan5x sin2x , when x is not equal to zero k , x=0 continuous at x=0?

For what value of k is the function

f(x)= tan5x sin2x , when x is not equal to zero

k , x=0

continuous at x=0?