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midterm_solutions - FWE‘D?‘ ”v1 MAT16B MIDTERM ONE...

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Unformatted text preview: FWE‘D?‘ ”v1 MAT16B MIDTERM ONE MONDAY FEB 1, 2010 Please write your name on the cover sheet. Write your answers on the exam paper. You may use one sheet of prepared notes. Calculators, cell phones, and other electronic devices are not allowed. Good luck! 1. Find all local maxim-d and minima of the function f(.’L‘) = 1'26” and indicate on which intervals f (14) is increasing and on which intervals it is decreasing. Be sure to indicate which critical points are local maxima and which are local minima. - , ,- - ““0 l (X) Z {'00: 71[’e’7‘>+97v6 7‘ (— I w m=o=zfer£D> MMW 7‘0cn2 2. Find the following antiderivatives: a. f (f + ff) (117 '2 b. [9—13—2- dm c. 21’ (ix x3+1 3. Suppose that, Write in terms of F(."L‘). 6'an I‘F(x)=¥(?<) ) £034": F(K)+C’ x 9/“!!un 0? R43 (since FCX) §3 amamHi I mcéFOO +ngp(x3)+ {Lem FOO: fiFC’O: 1% {a 397/5 'Xme 45$“ , 2%* C/ 7 ‘gwfi o , 5593+ C yum!) MM aznqu 149mm "/ 1“ “WM" 4. Find the values of the following definite integrals: a. £32 005(1‘) d); b. fofiw sin(;1:2) (is: ‘ ”gsinh/fi . (,. jg) ”7‘7;— (LL :— ~§I “905 (Xy/OFL: 7tz ~ C) MAX 0 2V3? I Yak/MN?) 7Cl : “0055/ : ~(~I)~—(~/):2_ D 5' What is the derivatiVe ”f “4”) = $111“) when .1? > 0. VVI'ite your answer in terms of ;L‘l“(-5)_ :9 ”7‘ = (“4 >02 t \ ‘ \ +Ael'lfiedeyw0ah'fle [fiat/1 310/6; 7C'(X ~ ZLnX .7: W) 'X :9 7~(x):4¥¥i.w>( 6. Let )=/m)? m where f(t )— — {mutanfl ) \Vhat is g(1 Note: arctan is the Inverse of the restriction of the tangent function to the interval [—7r/2, 7r/2]. mozfl f’ww : :Hw/J ‘2 flU—~Ho) fieoauire 750n(0) :0 and ‘fan(%) 2/ :2) aVc-fan[c2):—O ono/ WOEOMI):% :> 7%)“ W0) : grown“) — avctnn ('0) “L “4 7. Find the equation of the line tangent to the curve defined by the equation 1/ 1n(y)+l' =0 at the point (—e,e). I ' FWD U ; yin-)3! *(fln 3)?» / :0 I V 7(/+fln\7>:’/ CL “Q \3 I x S (h [\ M ...
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