Test1Solutions

Test1Solutions - 1) (20 points) Evaluate the following...

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Unformatted text preview: 1) (20 points) Evaluate the following limits. When appropriate, please specify either —00 or 00. _2 00 a) +4PQI flay (My .14 Km MM" (5') x—W X "‘ XW" I ( oo : m )(aoo X :4 um 26%) V X900 "7' (1)3211.” Jr woe ‘ 00’ 0 f3” Xe“: Z” 3% +7/95 x9420 yaw" e I; m ._.”_X ya-oo '6' e)1-i1})1‘(l+sinx)£ [00 , 12 73<l+fluoX> £0». _L E 12”” I+LIJW< _ x90* I g r | .M .1 X"0‘*[/m1 I ‘8 2) (30 points) Evaluate the following integrals: a) Ixedx wx WLZXM b) Icosxsin(sinx)dx q 1 X M:¢02XM fmum ‘—Couu-+C - MD<M><>+ Q c) Ix 1n xdx qflbmx M: XM ‘ X‘ @z‘éd/k V‘ 2* W 35 7,15,”- JZM ’L X1 X ’z/amx’ ;"+C d) [sin2 accos5 xdx fm‘x @013 C(AXM fox/nix (il-mz.x)LCe&A/M (Aij fléq-‘kada x+2x+l )Ix(x2'+9)dx 4, WX 2)“ “41+ BwC NV”) >« w x2+2x*/: Am Wfiwck sub .x:() ‘9 1': 9A Coefflow‘s Cod/\ru'mfi 1=A+8 02. 13:3 7 fl Ixleé—l dx 3)(15 points) Find the area ofthe region enclosed by the curves y = 2cosh(x / 2) , y = l, x = —3 , and x = 3 . Your solution must include a sketch ofthe region. 4) (15 points) The half-life of plutonium~239 is 24,360 years. If 10g of plutonium is released into the atmosphere by a nuclear accident, how many years will it take for 80% of the isotope to decay? v-k/E , , 2 7: (fl? 6 WAC/‘6, k ‘ @— ,7, 5) (20 points) Consider the function f(x) = e"(ex — l). a) Identify the domain and’x- and y-intercepts of y = f (x) . 7 M0 fills con Had] +/ Q 5 *9 OmQ m “i if whiz/rep"? 3 g“) 1673 'l) y— ,xyfercepfs ’ 6 ‘18): I) ’0 : 0 l b) Identify the horizontal and vertical asymptotes (if any) of y = ‘ (4/0 dis COni-(nunLIeJ ——>> A/O vufl'ml asym/Qf'ofefj % 6*(8 Y-’);OO ){ . ‘ MorIVZO/y‘Lai 'l 063a?“ 1/; 53700 2*(8 ‘/):0 K'm" c) Identify the coordinates of the relative extrema and inflection points. C/‘iilcql fizz/#55 KIQFO infleciia/t ’03:)381 KIKX):O (“Eelx‘e * 100526 Z;Cw y f‘MQezCex "64)» W3 =QVVCZGX“) Zea/:0 6": f7: (1) Sketch the curve, y = f(x) , plotting the p0int(s) and asymptote(s) found in parts a - c. ...
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Test1Solutions - 1) (20 points) Evaluate the following...

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