# Math203-FinalExam-Winter-2015.pdf - CONCORDIA UNIVERSITY...

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CONCORDIA UNIVERSITYDepartment of Mathematics & StatisticsCourseNumberSectionsMathematics203AllExaminationDatePagesFinalApril 20153Instructors:H. Greenspan, J. Nam, B. RhodesCourse ExaminerS. Vikram, Y. ZhaoA. AtoyanSpecialOnly approved calculators are allowed.Instructions:Show all your work for full marks.MARKS[11]1.(a)Letf(x) =x2-4 andg(x) =4-x. Findgfandfgand determine the domain of each of these composite functions.(b)Find the range of the functionf=e2x+ 2ex, the inverse functionf-1,and the range off-1. (HINT: assumeex=uto see how to findf-1)[10]2.Evaluate the limits:(a)limx→-2x2-x-64-x2(b)limx0x+ 9-3xDo not use l’Hˆopital rule.[6]3.Find all horizontal and vertical asymptotes of the functionf(x) =|x|4x2+ 1-2x2x2-3.[15]4.Find the derivatives of the following functions:(a)f(x) =2x5-x3/2x2(b)f(x) = lnx4x-3(c)f(x) =e3+ arctan(ex-e-x)(d)f(x) =ex1 + cos(x2)(e)f(x) = (1 +x2)2x(use logarithmic differentiation)
MATH 203Final ExaminationApril 2015Page 2 of 3[15]

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