If $\frac{dy}{dx} = (\ln 5)y $  with y(0) = ln 5, then what is y(1) equal to?

Consider the following in respect of the function f(x) = 10^x :

1. Its domain is (-∞, ∞)

2. It is a continuous function

3. It is differentiable at x = 0

Which of the above statements are correct?

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?