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Quiz 7 soln - Math 1A — Quiz 7 — Quiz/7 lNC/S Total/10...

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Unformatted text preview: Math 1A — Quiz 7 — March 21, 2008 Quiz/7 lNC/S Total/10 NAME ll Find the value of sec (tan‘ 12) Le: tan’ ‘ 2 = 9 then 2 = mine so we can draw a triangle: l 0 V“— with hwotenuse \/§ since mane =7 -1 _ _;_i_£_fi_ Thensec(mn 2)_Sece’cose_£—A_ 1 _\/5 fl 1 H 2‘ Find the derivative of each of the following functions. a) y=cos“(e7") y’z— , INF] 321.2 i e) b) y=ln(cosh3x) y’= 1 ~sinh3x-3 cosh 3x 1 . _ r I o) y= . _, =(sm 1)6) so 5111 x - 2 y’—— 1(sin'1x) 3, Find the limit 3) lim tim“(lnx) since lim lnx=— oothen X—o 0' x—H’J' lint}. tan‘ 1(In x) = — 3% (See the graph of tan‘ ’ in the book) . wshx . e‘+e"‘ . 1+e‘7” 1 11m =11m =12m = b) x—vzo ex x—om 23: pm, 2 ’2— 0 lim 4 asxHoowegetg...indeterminate X~°°ln(1+2e‘) 00 we better use I ’ Hopital ’ s: so thelimit becomes lim 1 = lim “-28 was 1 ‘22,, mm gex =lim 1+1=1 xq “’26" NOTECARD BONUS QUESTION: (1 point) Evaluate the limit . x“ — ax + a ~ 1 0 . . 11m —~——2— as x —> 1 weget — . . l mdetermmate x —v 1 (x _ l) 0 we better use I ’ Hopital ’ s: 11v 1 _ so the limit became: lim —a and asx —> 1 x A» 1 2x — 2 . 0 , . we still get — . . . Indeterminate 0 so we better use] ’ Hopital ’ s again: . _ _ Z _ so the limit becomes lim1 5% = gig—1) ...
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