calc1-finalexamf08 - from the plane to the radar station is...

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I Math 111 F'INAL EXAM I)ecember 17,2008 Read each problem carefirlly. Show all your work for each problem! No calculators! 1. (16 points) Find the derivatives of the following fimctions (do not sinrptiry) a) U: (e2,)(csc,r/6) b)z:W c)u:frcosr d)u:f smt2at 2- (8 points) Find the volume ofthe solid obtained byrotating the region bounded by A:12, U:4 and t:L aboutthey-"it". 3. (12 points) Evaluate the following integrals "1 f gr'- si,nr) d,x b) [ [t""" y)(tany) + jZ,.']av d I, # * (l6points) Given the function U : # a) find all asymptotes b) find the intervals on ufiich the function is increasing or decreasing, c) find the intervals on ufiich the function is concave up and concavi down" and d) sketch a graph of the firnction labeling local maxima, miuima and inflsclisn points (ifthey exist). (8 points) A plane flyine horizontally at an altitude (heighg of 3 miles and a speed of 600 miles f
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Unformatted text preview: from the plane to the radar station is increasing wtren it is b miles awayfrom the radar station. (12 points) Evaluate the following integrals ,) I: v'y'riav al [ #*c2(!) ar "),[i ffi^. : 7. (12 points) Evaluate the following limits: n, lr4ffi c) tim (tn t)tan(*) d) tim r* t + l + ' . z ' ' f i - - l * -)" (8 points) Find 7, ntthe following curves a) Y3 : tt * 2x2y * 3 as a function ofx and y (byusing implicit di:fferentiation) and b) r - e - sec20, U:2-tan20 asafunctionoftne pammeter0. (8 points) The top and bottom margins of a rectangular poster arc 2 i,nches and the side margins are 1 in'ch.If the area of the printed *utrtiuf on the poster ( in the shape of a rectangle) is fixed at I28irrches2 find the dimensions (engthanO width) of the poster with the smallest area Show that the area of the poster iia minimum. 4. 5. b) lim (I _ tt ' U-o \Y srnYl 8. 9....
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