Let \( f(x)=\left\{\begin{array}{cc}\frac{\ln (1+2 x)}{x}, & \frac{...
Let \( f(x)=\left\{\begin{array}{cc}\frac{\ln (1+2 x)}{x}, & \frac{-1}{2}x0 \\ 2 \cos x, & x=0 \\ \frac{e^{2 x}-1}{x}, & 0x1 \\ e^{2}-1, & x \geq 1\end{array}\right. \)
then :
(a) \( f(x) \) is continuous at \( x=0 \)
(b) \( f(x) \) is not differentiable at \( x=0 \)
(c) \( f(x) \) is continuous at \( x=1 \)
(d) \( \lim _{x \rightarrow 0^{+}}[f(x)]=1 \)
[Note : \( [k] \) denotes greatest integer less than or equal to \( k \).]
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