​ Let ƒ : R → R be defined as. f(x) = {x^3/(1-cos2x)^2 loge[1+2xe^-2x/(1-xe-x)^2], x ≠ 0 α, x = 0 If ƒ is continuous at x = 0

Question

Let ƒ : R → R be defined as.

f(x) = \(\begin{cases} \frac{x^3}{(1-cos2x)^2}log_e[\frac{1+2xe^{-2x}}{(1-xe^{-x})^2}], & x\neq0 \\ \alpha, & x=0 \end{cases}\) 

f(x) = {x³/(1-cos2x)² log_e[1+2xe^-2x/(1-xe^-x)²], x ≠ 0

α, x = 0

If ƒ is continuous at x = 0, then α is equal to :

(1) 1

(2) 3

(3) 0

(4) 2

Answer 1

Answer is: (1) 1

For continuity