CQALCULEN LeN Limi te SuiU \( \lim _{x \rightarrow 3} \frac{3}{x-3} ; \) \( \lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3} \) \( \lim _{x \rightarrow 1} \frac{x+1}{x-1} \) \( \lim _{x \rightarrow-2} \frac{x^{2}-3 x+1}{x+2} \) \( \lim _{x \rightarrow 1} \frac{-x-2}{x^{2}-4 x+3} \)

A. The critical number of \( f(x) \) B. Find the intervals on which \( f \) is increasing and decreasing by using the first derivative test Find the local maximum and minimum, if they exist by using the first derivative test Find the intervals on which \( f \) is concave up and concave down Find the inflection points of \( f(x) \)

20. \( \int x \tan ^{2} x d x \)

Integrate the following: \( \int x e^{2 x} d x \)

If \( m \in \mathbb{R} \) and \( \lim _{x \rightarrow \infty} \frac{(m+5) x^{3}-x+4}{3 m x^{3}-2 x+9}=2 \), then \( m= \)

What is the solution to the following differential equation, subject to the initial condition \( y(0)=2 \) ? \( \frac{d y}{d x}=6 x+6 \)