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Given the function G(x) where we denote it's derivative as , looking at the definitions that have been assigned to the individual functions, show what integrating the following integral would give us  

 

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1. (16 marks, 2 for each part.) The problem consists of 8 short-answer questions: V22 +12 - 1 (a) Evaluate lim - or determine that it does not exist. In the latter case, write DNE as answer. 1+2 -1 Answer (b) Find values of a that would make the following function continuous everywhere, or determine that no such value exists. In the latter case, write DNE as answer. g(x) = ( 22+2 2+1 ar if I 1. Answer (c) Find the derivative of y = r" lnr. Answ (d) Find the equation for the tangent line to the curve z-y + xy2 = 2 at (1,1). Answer (e) Use linear approximation to estimate (0.998) Answer if any exists. Write DNE if none r2 - 4 (f) Find the vertical, horizontal or slant asymptotes of f(x) = exists. Answer (g) Find any local maxima and minima of h(x) = r- in the interval (1,4). Give both r and h(2) values and state whether it is a local minimum or maximum. Answer (h) On which part of the interval [0,1] is f(x) = et sin x concave upward? Answer

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