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22 Jan 2018

(5) Determine whether each series is convergent or divergent, and give a valid reason for your answer. On

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Lelia Lubowitz
Lelia LubowitzLv2
23 Jan 2018
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2. Determine whether each integral is convergent or divergent. Evaluate those that convergent e Vx ) dx [5 marks] i Var

5. (22 pts) x² - 4 x-5 if x < 2, Let g(x)= sin (1 x) if x 22. (I) Evaluate the limit or state that it does not exist. If the limit does not exist, explain why. Show your work. (Note: Possible answers include + cor -.) (a) (3 pts) lim g(x) = ; (b) (3 pts) lim g (x) = (II) (2 pts) Determine whether g has any horizontal asymptotes. If so, write the equation (or equations) of all horizontal asymptotes. (III) (4 pts) Determine whether g has any slant asymptotes. If so, write the equation (or equations) of all slant asymptotes. (IV) (2 pts) Determine whether g has any vertical asymptotes. If so, write the equation (or equations) of all vertical asymptotes. (V) (8 pts) Determine whether g is continuous at 2. Use the definition of continuity, when justifying your answer. SHOW YOUR WORK.

5. (a) (5 points) The figure below shows graphs of two exponential functions. Match each of the following two functions to a graph. (1) f(x) = 2* : Graph (I or II) (2) g(x) - 3*: Graph_ (I or II) 7 05 15 2.5 35 45 (b) (15 points) Given f(x), g(x), h(x) below. X 0112T 3T 4 f(x) 10 13 16 19 22 g(x) 4 8 11 9 6 | h(x) 2 3 4.5 6.75 10.125 (1) (5 pts) Determine which function could represent an exponential function. Show your reason. (2) (10 pts) Find the explicit formula for the exponential function.

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