Compute limits and carry out some basic proofs. Compute derivatives and use them in applications such as computing rates of change, finding extreme values, sketching graphs of functions by finding intervals of increase/decrease, concavity and asymptotes, use transcendental functions including logarithms, exponentials and inverse trigonometric functions effectively. Compute integrals by the Riemann Sum definition and use it to make approximations. Make use of basic techniques to compute proper integrals.