## First Midterm

## Fall 2001

1. Find all of the points where the tangent plane to the curve

z = x^{2} + 3xy + 2y^{2} - 3x - 5y + 4
is horizontal. What kind of a stationary point is this?

2. Find L_{4}, R_{4}, and T_{4} for

Find the integral by using the Fundamental Theorem of Calculus.
Compare the errors you get with the errors predicted in Theorem 1.

Find the following integrals. Show your work.

13. Derive the four reduction formulas on p 511 of the text.