1.Find $\frac{dy}{dx}$ if $x^2 + y^2 = 25$ using implicit differentiation.
2.Evaluate the integral $\int \frac{x}{x^2 + 1} dx$.
3.A right circular cylinder has fixed volume $V$. Find the ratio of height to radius $h/r$ for minimum total surface area.
4.Evaluate $\lim_{x \to 0} \frac{1 - \cos(x)}{x^2}$.
5.If $y = e^{ax} \sin(bx)$, prove that $\frac{d^2y}{dx^2} - 2a \frac{dy}{dx} + (a^2 + b^2)y = 0$.
