Practice final exam calc 1

# Practice final exam calc 1 - LBS 118 FINAL EXAM ’ Name V...

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Unformatted text preview: LBS 118 FINAL EXAM' ’ Name:' V ~ “ CALCULUS I Student 5: _ m 31‘ " TA's name: _ ’ ‘ ' . ————— _ - Please show xqur work clean! on all problems to earn maxunum credit. USE THE GRAPH SHOWN TO FIND THE LIMITS: (If the limit does not exist, EXPLAIN why it does not exiSt) 1) lim i(x) x -> + 00 2) ‘ Iim I(x) " X ~—> — 00 3) lim I(x) x -—> 1' 4) ‘ Iim i(x) I X —-> I EVALUATE THE FOLLOWING LIMITS ALGEBRAICALLY: 7 (You must SHOW WORK for credit and give EXACT answers.) 5) Iim e"-1-x-gx2/2) , , x—>1 x3 6) lim x-2 x->~1 x2+4x 3 7).2‘ “m ._J.. -. 2 x—>1 x-1 x2-1 FIND dy/dx FOR THE FOLLOWING FUNCTIONS: 8) y =- 74x 2 - 7.x <— You do not have to simplify your answer to this. ‘ J7x-3 9) x3+x2y+4y2=6 GIVEN THE CURVE y = x4 — 4 x3 FIND ALL OF THE FOLLOWING: 10) On what intervaKs) is the curve INCREASING? 11) On what interval(s) is the curve CONCAVE UP? I 12) Give the values oi any LOCAL EXTREMA and tell where they occur. 13) Give the values of any INFLECTTON POINTS and tell where they occur. FIND THE FOLLOWING INTEGRALS: 14) 5 xzsin (5x) dx 15) x3+x2—12x+1 dx x2+x- 12 r 7 _ . 16) f x \I 1+x2fdx I -<—- Give EXACT answer. NO DECIMALS. 0. SOLVE THE STORY PROBLEM: 17) A ladder to it long rests against a vertical wall. lithe bottom of the ladder slides away from the wall at a rate oI 1 "/3, how fast is the top ol the ladder sliding down the wall when the bottom of the ladder is 6 it lrom the wall? GIVEN THE GRAPH SHOWN HERE, SET UP (BUT DO NOT EVALUATE): ' 3 J! , wacI: g=élx (0'1. x=12ép 18) An integral with respect to X that gives the area between the two curves. 19) An integral-with rm. to Y that gives the area between the two curves. 20) An integral which gives the volume generated when rotating the shaded region around the X—AXIS. _ USING THE WASHER or DlSK METHOD * 21) An integral which gives the'Volurne generated when rotating the shaded region around the X-AXlS USING THE SHELL MEIHQD ' 22) An integral which gives-the volume generated when rotating the region around the Y-AXIS. . USING THE WASHER or orsx METHOD.‘ » ' 23) An integral which gives thegvolume generated when rotating the shaded region arorind the Y-AXIS. USING THE SHELL METHOD ‘ ...
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## This note was uploaded on 03/19/2008 for the course LBS 118 taught by Professor Nichols during the Winter '01 term at Michigan State University.

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Practice final exam calc 1 - LBS 118 FINAL EXAM ’ Name V...

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