Consider the following statements

statement 1: $$\lim _\limits{x \rightarrow 1} \frac{a x^2+b x+c}{x^2+b x+a}$$ is 1

(where $$a+b+c \neq 0$$).

statement 2: $$\lim _\limits{x \rightarrow -2} \frac{\frac{1}{x}+\frac{1}{2}}{x+2}$$ is $$\frac{1}{4}$$.

If $$f(x)=\left|\begin{array}{ccc}\cos x & 1 & 0 \\ 0 & 2 \cos x & 3 \\ 0 & 1 & 2 \cos x\end{array}\right|$$, then $$\lim _\limits{x \rightarrow \pi} f(x)$$ is equal to

At $$x=1$$, the function

$$f(x)=\left\{\begin{array}{cc} x^3-1, & 1< x < \infty \\ x-1, & -\infty< x \leq 1 \end{array}\right. \text { is }$$

The right hand and left hand limit of the function are respectively.

$$f(x)=\left\{\begin{array}{cc} \frac{e^{1 / x}-1}{e^{1 / x}+1}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0 \end{array}\right.$$