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# m116b01a - 1 c [email protected] MATHA116 Survey of Calculus...

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Unformatted text preview: 1 c [email protected] MATHA116, Survey of Calculus, Bonus Problem Updated on October 26, 2006 Get help whenever in doubt! Direction. VIII-1. I am posting this bonus problem for those who want to earn extra credits for this course. The points you earn on this problem will be added into your quiz total. Please turn in your answer in class on Thursday, Oct. 26, 2006. N Important: Direction. Question VIII-1. (50 points, bonus) If f is differentiable at x = 1 and f (1) = 6, evaluate the following limit f (x) - f (1) x1 x-1 lim You must show your mathematical work in order to earn any credit. An answer alone, right or wrong, will receive 0 point. W ork VIII-1. Here is the solution with all the mathematical work shown. rationalization f (x) - f (1) lim x1 x-1 = = f (x) - f (1) x+1 lim x1 x-1 x+1 f (x) - f (1) 2 lim ( x + 1) 2 x1 ( x) - 1 dif f erence of squares (1) (2) = x1 lim f (x) - f (1) lim ( x + 1) x1 x-1 ( 1 + 1) = 6 2 = 12 (3) def. of der. direct subst. = f (1) (4) where by the definition of a derivative, f (1) = The answer is, lim f (x) - f (1) x-1 = 12. (6) f (x) - f (1) =6 x1 x-1 lim (5) x1 end of Bonus Problem ...
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