Monotonicity

Q.

If the function f(x) satisfies $\underset{x\to 1}{\text{lim}}\frac{f\left(x\right)-2}{x^2-1}=\pi$, evaluate $\underset{x\to 1}{\text{lim}}$ f(x).

Q. Let $h\left(x\right)=f\left(x\right)-a\left(f\right(x){)}^2+a(f\left(x\right){)}^3$
for every real number $x$.
If $f\left(x\right)$ is strictly increasing function, then $h\left(x\right)$ is non-monotonic function given

1. $a\in (0,3)$
2. $a\in (-2,2)$
3. $a\in (3,\infty )$
4. $a\in (-\infty ,0)\cup (3,\infty )$

Q.

Which of the following types of functions are called monotonic functions

1. Strictly increasing

2. Monotonically increasing

3. Strictly decreasing

4. Monotonically decreasing