Find the value of f(0), so that the function f(x)=(2 x- sin -1 x/2 x+ tan -1 x) is continuous at each point in its domain.

Question

Find the value of f(0), so that the function f(x)=(2 x- sin -1 x/2 x+ tan -1 x) is continuous at each point in its domain. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f(0)= displaystyle lim x arrow 0 (2 x- sin -1 x/2 x+ tan -1 x), (0/0) = displaystyle lim x arrow 0 (2-(1/√1-x2)/2+(1)1+x2)=(1/3)

Q. Find the value of $f (0)$ , so that the function $f (x) = \frac{2 x - s i n ^{- 1} x}{2 x + t a n ^{- 1} x}$ is continuous at each point in its domain.