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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"1xgx2/2) , ,
x—>1 x3 6) lim x2
x>~1 x2+4x 3
7).2‘ “m ._J.. . 2
x—>1 x1 x21 FIND dy/dx FOR THE FOLLOWING FUNCTIONS: 8) y = 74x 2  7.x <— You do not have to simplify your answer to this. ‘ J7x3 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 integralwith 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 XAXlS
USING THE SHELL MEIHQD ' 22) An integral which givesthe volume generated when rotating the region around the YAXIS.
. USING THE WASHER or orsx METHOD.‘ » ' 23) An integral which gives thegvolume generated when rotating the shaded region arorind the YAXIS.
USING THE SHELL METHOD ‘ ...
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 Winter '01
 nichols

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