1: Name:
Class January 9, 2008 To Do for Friday, January 11, 2008 1. Read Sections 5.6, Integration by Parts 2. Complete this handout to turn in. You may do this handout using your text or notes. You may discuss general differentiation and integration strategies with others, but you are to do the problems on your own without looking at anyone else's work. This handout represents some of the topics and techniques that you should have learned in Calculus I and serves as a review of Calculus I material.
Calculus I Review
1. If f ( x ) = 4 x 2 + 5 , prove that f ( x ) = 8x using the definition of derivative: f ( x + h) f ( x ) f ( x ) = lim h0 h
2. Find the derivative the of following functions. f ( x ) = x 2 cos ( x ) + e 3
f ( x ) = 5x 2 + x + 3 f ( x) = 3x 2 + 2x cos ( 4 x )
f ( x ) = sin 3x 2 + e5 x f ( x ) = sin 3x 2 e5 x
( )
( )( )
dy when x = 1 and dx
3. If the equation 2xy + sin ( y ) = 2 defines a function y = f ( x ) find
y=
2
4. Find
dy at the point (1,1) if 2y 3 + 4xy + x 2 = 7 dx
5. Find the antiderivative of the following functio...