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# Midterm2v1GradingKey - L SMWS& growling Keg lVlidterm II...

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Unformatted text preview: L SMWS & growling Keg lVlidterm II Tuesday, 1. (10 pts) Suppose that electricity is draining from a capacitor at a rate that is proportional to the voltage V across its terminals and that, if time t is measured in seconds, = —1%V. Solve this equation for V, using V0 to denote the value of V when t = 0. How long will it take the voltage to drop to 50% of its original value? {- _/’a Sad/ﬂan : 71¢ (av 74’" 09W 0’4”?! M W0: 75 'Ml ‘L‘imc. T fill/49!?" e 4 WM ﬂit—“Kejé— +515 (IL : ’ .720 é“ ':/o&z < +2F‘b M~ 2. (15 pts) Find the integral f5“ tan3(x) dx Ty — 1/9 Z )4— M/ @ .2 s 1-“, (Sgcx—I _ E E ran-I 5‘ ¢M3Xaéc r..- [fmxlsﬁo 7y, ' O D :- __ I“ tmxseczxoét — l th4‘ ’ #4' a D GE..- LfgL‘Jr-z -(o+4r)=i-%Z- 3. (l0 pts) Find the derivative of the function 1‘ y = (t2 + 2t)tanh(t+ 1) 8mm: g; W+ (11¢) sec/16%)): 3 [:75 7/15 dI 4. (10 pts) ff“ Icosﬂn x) (Hint: use substitution 2 = and then multiply and divide new integrand by sec 2 + tan 2) ._ 1 . e 3‘ ,1 x E”): a! __ SQMM . /‘ ’—’ “‘1? a —‘ / I .z mla") ,_ @ :: Ia~ l Sta—lg ++"’LT% I ’ﬂx— [Slcﬂi—i‘ma) :— V “45 I“)? z z W 5% s 22x2=4zwz= ; V/ ‘43 4 i- : We); (W<')‘W)3=% 3 ® I 7. (15 ts) p 0 wixE-Q-mlx‘imz 2 3 5+5 'V ° _‘5’ = y'liims‘x 061.9%}. {290%00C: 0—9: W‘Xl: O O / : n (mama); (SW; 8. (10 pts) fflnxdw = -€. is M jeﬂm 0695; a!” £6ny )6— ‘rxé’aem =xﬁix-gc/Cz 4 1 4 : (8 ae’€)— : e are—8+] 5196 1 9.10tEt“ “d‘t d: ( ps) X1a01e1fl+sinx x (Hint: multiply and divide by 1 — sin \$er Lib—BS L'séntxaghgi—samx AX: H-Sinzr, i-‘ﬁmx @Smclx 06x 1‘ 4 Mix 60096 ...
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Midterm2v1GradingKey - L SMWS& growling Keg lVlidterm II...

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