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Quiz2num1soln - 1 Find the limit lim tan(1 —— sm(t...

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Unformatted text preview: 1. Find the limit lim tan (1 —— sm(t) ) t—*0 t V/(OL 5% U€€Z< Hwy; 1/12; 5/;[%): I l , O - 7 51(n(< 7Lcm {O3 — 511/0) 1' ’1', ’ O ' (0570 j ’3 b7, C®n I'm/#7 07C fan/X) Q) X ; .O ’ Wf 7cYZ ail/J - - “m 21$?) , mm = 0 {go {MK/ ’ " 710"/’ «‘90 f * ] 2. Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of d2y/ d1:2 at this point. :10 = t —— sin(t), y =1— cos(t), = 7r/3 277’35) gig : 5%; (S‘MHW (I ~co5/fly) : COS/7}) (I -cos/z‘)jI *— SIVAW) /l~cos/i)).z it J 1 mm (1-way) ~ sin/a3 .— Cos/0-5032613— MB- ~(z - cos/m (”ms/fl)" (I cos/ml (1 com» -I 4031*)! . 91 __ _—__L__ 1 1 9:1] :5; FL) (1- cos/ml 9X1”? , ’- 3. Find the derivative of y with respect to the given independent variable. Li 7117 ln5 = 1 y og5 (3x + 2) n j 3 [125 [Oj§[3j:2] I I“? Iowa") _, [Ojséx 03] _)__ n 3 y 3x+Z~3¥ _,_ : 2x 2(3X‘+Z) ‘ Wx) _ 3X1 *ZX 4. Find the derivative of y with respect to the appro- priate variable. y = ln(:102 + 4) — antan—1 (—325) / \ .435, I I ./ y: .QX ——<+cm(z>‘ix ’+(X)z Z >31”! 2 7.x _ X —. MM “EN/3 , “*7: 'X’L‘W‘i 2+2— X 3.2:, - and/g?) ~ 2 7. 1 )3“, (fix -. fl) ...
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