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Unformatted text preview: MATH 3B EXAM I PRACTICE January 13, 2011 JEFFREY STOPPLE In these notes you will come up with your own practice exam questions. This will better help internalize the material. You should solve your own exam, or if you have a study partner you should switch and solve each other’s exams. For best results, repeat as of- ten as necessary. Problem 1. Relating to § 4.9 on Antiderivatives, from Math 3A you should know the derivatives of the following functions: x n , log | x | , exp( kx ) = e kx , sin( x ) , cos( x ) , tan( x ) , cot( x ) , sec( x ) , csc( x ) , arctan( x ) , arcsin( x ) , sinh( x ) , cosh( x ) . Select four of the antiderivatives (or indefinite integrals) below. An- swer based on your knowledge of the above. Verify that your an- swer is correct by computing the derivative. Z x n dx = for x 6 =- 1 Z exp( kx ) dx = Z x- 1 dx = Z sin( x ) dx = Z cos( x ) dx = Z sec 2 ( x ) dx = Z csc 2 ( x ) dx = Z sec( x ) tan( x ) dx = Z csc( x ) cot( x ) dx = Z 1 1 + x 2 dx = Z 1 √ 1- x 2 dx = Z sinh( x ) dx = Z cosh( x ) dx = 1 2 JEFFREY STOPPLE Problem 2.Problem 2....
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This note was uploaded on 01/21/2012 for the course MATH 3B taught by Professor Shu during the Spring '08 term at UCSB.
- Spring '08