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13 Nov 2019
Please explain and answer every part of the question:
Presentation problem 4. (14 points) Consider the function f(x) =å for x E [-1,0) and let A(x)-, f(t)dt for x E [-1,0). (a) (4 points) Is the function f(x) positive? What is limx o f(x)? Does it have vertical asymp- totes? Approximately sketch the function (no need to study its extremal points). (b) (2 points) Compute A(x). (c) (2 points) What is the value of limoA(x)? (d) (6 points) Express in your words and/or pictures what liA(x) represents in terms of areas under the graph offlx). Can a positive function with a vertical asymptote have a finite underlying area?
Please explain and answer every part of the question:
Presentation problem 4. (14 points) Consider the function f(x) =å for x E [-1,0) and let A(x)-, f(t)dt for x E [-1,0). (a) (4 points) Is the function f(x) positive? What is limx o f(x)? Does it have vertical asymp- totes? Approximately sketch the function (no need to study its extremal points). (b) (2 points) Compute A(x). (c) (2 points) What is the value of limoA(x)? (d) (6 points) Express in your words and/or pictures what liA(x) represents in terms of areas under the graph offlx). Can a positive function with a vertical asymptote have a finite underlying area?
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Reid WolffLv2
2 Apr 2019