Ernst_Test_1_Fall_2007-1

# Ernst_Test_1_Fall_2007-1 - Show ALL steps a f(e3X 3 x3 3 dx...

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\o~ ~f\C1~ ' MATH 102-02 - TEST 1 \' I NAME: J!.~I> /l'-""41) MS. ERNST . FEB. 5, 2007 1. (7 pts) Given fl/(x) = 2x + ;3' f'(1) = % and f(1) = -i· Find f(x). -) 1- 1. ~ ..• -"1.- X 7.. r ., ~. :.. f _ Z. . . i-/-I 'J/) ~_.I J -t '-2 ..•.(, L~-] 2. (8 pts.) Evaluate the integral using the Limit-Sum Definition. (Riemann-Sum) o f (x2 + 2x) dx o / 3. (7 pts.) Find g~ ~) given g(x) = J Jsint dt ;' If) ~ ~ (.7.) " I~ ) f' /Ij:, \1 ••. ;0\$ l (oS '"-- l. \ - -- - 0

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4. (10 pts.) Find the area bounded by the curves. (Sketch the graphs) y = e', y = x - 1, x = 0, x = 1 'E:" - \ t- G) ( 'i/0 Sa. (16 pts.) Evaluate the integral numerically using the Trapezoidal Rule. SHOW ALL STEPS. (Round your answer to 4 decimal places.) 2 f 2x 2 dx, n-4 o x +4 - '" \1\ 53 5b. Find the exact value of the integral. 'C '- .••• b- '" ?(~\ Y " L\; c~ YJI) \ ~) ~(~) l~ ..L ~ ~ - I : )'- •. I, L\ r::;z ;I? 5 : 8;(j B ~ - -;:j N +- --- /,,2. L{ "II --- r /'2. 'L (2,; ",'1. I 8: ,.Jl. ~~'YI ~ - " v \ N N 'l\;~ N l\ l\;~N r-l t l l../'I 2-
6. (32 pts.) Evaluate the integrals.

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Unformatted text preview: Show ALL steps. a. f (e3X + 3' + x3 + 3) dx r \ -r e-,'}. . b. e x+ x3 f x2 dx 'f. . '!. .,-1. . .••-)< 'j.,1.-c. f sec2 (3x) dx d. x dx J .J9+x2 7. (20 pts.) Set up but do not evaluate the integrals that would find the volume of the solid formed by rotating the region bounded by the curves y = E, y = 2-x, y = O(x-axis) about the lines; [ DO NOT EVALVA TE THE INTEGRALS] [SKETCH THE GRAPH] a. y-axIs b. X -aXIS n J~. 6,/< __ Aswe. . •• f v~-rr)o (\2-'f~-,/'1.) Jy c. x=2 \$'1l6L'-, v.,. 11')0 7..(z-y-yt.) dy ~7<:='"'\ ' •.. ~ .-....-;.---. L\ f. '-' p,>~ri.~ v'~1T ((1._y'l.)'L-It-lt.-'i'))1.\ J • ) y...
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## This note was uploaded on 11/23/2009 for the course MATH 102 taught by Professor All during the Spring '09 term at Kettering.

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Ernst_Test_1_Fall_2007-1 - Show ALL steps a f(e3X 3 x3 3 dx...

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