$$\lim _\limits{x \rightarrow 1} \frac{a b^x-a^x b}{x^2-1}=$$

If the function

$$\begin{array}{rlrl} f(x) & =3 a x+b, & & \text { for } x<1 \\ & =11, & & \text { for } x=1 \\ & =5 a x-2 b, & \text { for } x>1 \end{array}$$

is continuous at $$x=1$$. Then, the values of $$a$$ and $$b$$ are

$$\begin{aligned} & \text { If the function given by} \mathrm{f}(\mathrm{x}) \\ & =-2 \sin \mathrm{x} \quad-\pi \leq \mathrm{x}<-(\pi / 2) \\ & =a \sin x+b \quad-(\pi / 2)< x<(\pi / 2) \\ & =\cos x \quad(\pi / 2) \leq x \leq \pi \\ \end{aligned}$$

is continuous in $$[-\pi, \pi]$$, then the value of $$(3 a+2 b)^3$$ is

If $$f(x)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x}$$, for $$x \neq \pi$$ is continuous at $$x=\pi$$, then the value of $$f(\pi)$$ is