MATH 211 Final: MATH 211 NIU Math211FinalForWeb
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1. (16 points) consider f (x) as defined below and complete the subsequent tasks. f (x) = (a) calculate x < 3. Make sure you support your claim with rigorous reasoning: (10 points) calculate x 2+5 x-50, (10 points) calculate lim. 25-x 2 x 5 x 13-11 x 2 lim. 3-5 x+7 x 2: (18 points) calculate the derivative of the following functions. Simplify only if: (16 points) calculate the derivative of f (x) = x - -x - 1 (a) f (x) = 1 - x + x 5 1 - x 2 + x 7 appropriate. (b) g(x) = ln(x) + 1 x 3 ln(x) (c) h(x) = ln x - e x: (20 points) sketch the graph of f (x) = x 4. List the coordinates of where the extrema or points of inflection occur. State where the function is increasing or decreasing, as well as where it is concave up or concave down.
