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Unformatted text preview: 1910  CALCULUS FOR ENGINEERS, F ALL 2011, PRELIM II 7:309pm, October 27, 2011. Answer the following 5 questions. Show all work. Closed book, no calculators; 1sided (8.5 x 11) cheat sheet is allowed  individually and uniquely handwritten (without collaboration)  will be collected along with the exams  will not be returned. Academic integrity on the part of each student is presumed. Violations will be dealt with swiftly and justly. 1.(10 pts each) Find derivatives for the following functions: a) x b) xe (x > 0) c) x arctan(ex ) 2.(10 pts each) a) lim Compute the following limits: ln (1  x) x0 arcsin x b) lim +
x0 3 x3 x 0 t3 dt c) lim (1/x)x x0+ et  1 d) lim xe1/x +
x0 3.(15 pts each) a) Compute the following integrals:
/3 2 tan x sec x dx b)
0 1 3 x3 dx c) x2  1 2 1 dx dx 2x  x2 4.(10 + 5 + 5 + 10 pts)
a) Show that the following function is onetoone, and has an inverse: f (x) = earctan x cosh x
b) What is the domain of c) What is the range of d) Compute f 1 ? f 1 ? (f 1 ) (1). 5.(20 pts) Calculate the volume of the solid of revolution formed by rotating the region in the xy plane between the curves y = e2x and y = ex , 0 x 1, about the yaxis. 1 ...
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This note was uploaded on 10/31/2011 for the course MATH 1910 at Cornell University (Engineering School).
 '07
 BERMAN
 Calculus

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