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mid3_sol - Problem 1[14 points Find the point on the curve...

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Unformatted text preview: Problem 1. [14 points] Find the point on the curve 3/ = ézz that is closest to the point (4.1). 'TLHAs A hm +MA abs‘alfi‘tfi Warn N" 5(1‘7— -" 4V4} (2 I 2) fr, +144 Close$" Fain+ . - » . 2?“; Problem 2. [14 points] Find the derivative of the following function. 2+cou :: 3 gm = f e‘ at: 2 7, u 2 H t 3%” g 6% 4+, .412 z : 9U (WWW) 62—4605sz Problem 3. [12 points] The curve 3; = f (2:) passes through (—1. 5) and the slope of the tangent. line to this curve at (x,f(:c)) is equal to 3:2 — 4. What is f(2)? Shave .( 46» MM 03 CY. $00) : {'(x): 333-4 ""“" 3 (7+5 71M»: «C(x) —_ x3 -—lL¥+ C, ‘‘‘‘‘‘ '5 FL, $<~n=~x +MC: r5 = 2.. :9 +00: {>4ng U--. 3 P+5 Pm: E'rP—Flt 2 ~ 3 F45 Problem 4. [12 points] Evaluate the following limit. , 1" 1"1 305.20%) I=l H €m=x“, Yf—H'CAY V‘ m mm = Qm iflm Av 7.. “-9 co ‘-\ t (’1 4:004)! U! ..... Problem 5. [16 points] Find the general indefinite integral. (a) [8 points]/<l+a:2+ Vii—x5)“ (b) [8 points] / aseczman3 zda: Le’r u: Jcpmx. The» du = Seczy Ax Problem 6. [32 points] Find the definite integral. 3 (a) [8 points] / la:2 —4|d.1: o I{ o €132 , +Vxev~ Xz~4£o :1; zsxes fin» 53420 f 3 '2. TM“ S3\x‘-a\lxc >Dz-Cx1-md¥¥$z (x4305! 4'75 —- - [1: 4X11 Kai—4x13 :— [ -:——8-o~§ + [qul’Q-Xi’gf} '2} — ‘---~ 4 p45 _ "'3 (b) [8 points] /; c (11133“ m u: w. Tm 4u=%°‘* a Vb be 56 C9”? Ax: K U50” ~~ ~ 72 p45 I ‘x _ QJ + l _ LA ‘ [7:39 ‘---- 1P}; a (d) [8 points] A 2:2:(a:2 - 3)5da: [91"- U‘: Xl-3 . x--— \\\\ ...
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