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Answer the following questions.

 

If and , find

 

If and , find .

 

If , , and . Find .    

           

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Ranti Timario
Ranti TimarioLv10
22 Jan 2021
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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

consider the function below. (if an answer does not exist, enter dne.) 

A) Find the intervals of increase and decrease.

B) Find the local maxima and minima.

C) Find the inflection Points.

 

1. (a) Let f(x) = xe-* Find f'(x) and simplify your answer. [4 points) (b) Let y=z® log2(x). Find dy and simplify. [4 points) [5 points) 8 - V163 , if 374 (c) For x > 0 let h(2) = 2 - k if x = 4 Find the value of the constant k that makes h continuous at x = 4.

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