1. Using the laws of logarithms and properties of summations, show that In II k=1 Ck! k=1 k=1 2. Findthefollowinglimitsbyusinglimitsyoualreadyknow,andconsideringorderofgrowth. Youdonot need to show work. (a) lim noor", when r > 1, when 0 co) b) lim -+00 02 (c) lim +2 - 178932t + 3.15 (d) lim e-(x-4)2 (e) lim -+0 1+ ex (f) lim c'e (g) lim In h) lim Vx2 + 6x 3. Findthederivativeofeachofthefollowingfunctions. Youshouldconfirmallofyouranswersarecorrect using a computer algebra system (such as Wolfram Alpha). You should be able to compute derivatives such as these with 100% accuracy. (a) f(x) = ex2 (b ) f ( 20 ) = ( e ) 2 c) f(t) = log12(5t) ebi d) f(x) = 1 + ebr pbx (e) f(b) = 1 + ex (f) f (x) = In (sin (1 + x))2 (5x x 2(-2x4 + 72 - 8)) g) f(x) = In(x2) h) f(x) = In(vx) . vac (i) f(x) = 1 4x2 (i) f( M) = x! 4. Supposethatasnowstormbeginsatmidnight, andthefunction f(t)givesthedepthofsnowininches on my driveway, where t is the number of hours past midnight. Interpret the statements f(2) = 3 and f'(3) = 2 in the context of this