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9. Which function is one-to-one and NOT onto? Circle the correct answer. f: Z +Z f(1) = 23 g: R +R g(x) = 13 h: RR h(x) = r2 r: RXR+R r(x, y) = x2 + y

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Nestor Rutherford
Nestor RutherfordLv2
13 Aug 2018
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6. Which function is a surjection but not an injection? h: R + (0,1] p: (0,00) + R f: R + R f(2)=e" 9: R +R g(2)=23 h()= 1+12 p()=r+

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

3. Consider the statement R=(Ex € Z) [(r² = (1 + 1)2) = (23 EZ)]. (a) Write the negation of R without using the symbol . You may use the symbols # and/or &, if necessary. NO explanation is needed. (b) Which statement is true, Ror-R ? Circle the correct answer. NO explanation is needed. R is TRUE -R is TRUE

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