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?

If a differentiable function f(x) satisfies $\mathop {\lim }\limits_{x \to - 1} \dfrac{f(x)+1}{x^2-1}=-\dfrac{3}{2}$ then what is $\mathop {\lim }\limits_{x \to - 1} f(x)$ equal to?