Math 1a03 C01 C02 C03 Fall 2011 Mcmaster University Practice Final Exam

Math 1A03 C01, C02, C03 Fall 2011McMaster University Practice Final Exam Duration: 3 hoursInstructors: M. Bays, L. Barto, D. HaskellGiven Name: Family Name:Student ID Number:Instructions{ Give full justication for your answers.{ Only the McMaster standard calculator, the Casio fx 991, is permitted. Problem Points Problem Points1 72 83 94 105 116Totalpage 1 of 16McMaster University Math 1A03 Fall 2011 Practice Final Exam1)Find the derivatives of the following functions. No partial credit will be given on thisproblem. a) f(x ) = arctan( x2)b) x+ sin( x) ln(x)c) e2xtan( x) page 2 of 16McMaster University Math 1A03 Fall 2011 Practice Final Exam2)Evaluate the following limits. No partial credit will be given on this problem.a) lim x! 0sin(x) xb) lim x!1 (2x2 x3)c) lim x! 2+ f(x ) and limx! 2 f(x ), where f(x ) = x2+ x+ 5, for x 2.Is fcontinuous at 2? page 3 of 16McMaster University Math 1A03 Fall 2011 Practice Final Exam3)Find the general forms of the following indenite integrals. No partial credit will be givenon this problem.a) Z1 x1=3 dxb) Z(2x+ 13) ln( x2+ 13 x+ 1) dxc) Z(e 2x+ 5) dx page 4 of 16McMaster University Math 1A03 Fall 2011 Practice Final Exam4)The speed v(t)