Let y = [x + 1], -4 < x < -3 where [.] is the greatest integer function. What is the derivative of y with respect to x at x = -3.5?

What is $\lim\limits_{x \to 0}x^3(\text{cosec} \ x)^2$ equal to ?

What is $\lim\limits_{x \to 1}\frac{x^3 - 1}{\sqrt x - 1}$ equal to?

What is $\rm \displaystyle\lim_{n \rightarrow \infty} \frac{a^n+b^n}{a^n-b^n}$ where a > b > 1, equal to?