(a) Consider the functions f, g : R R defined by the expressions f(x) =...
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(a) Consider the functions f, g : R → R defined by the expressions f(x) = 10a? + 60r – 50 and g(x) = 6x – x2. Find 40F 20 4. 20 40 10 (x2  6x+5) 100 (x6) x Figure 1: Plot of the two quadratics. (i) the area under f(r) and above y = 0; (2 marks) (ii) the area under g(x) and above y = 0; (2 marks) (ii) points ri < r2 where f(x) and g(1) intersect; (4 marks) (iv) the area between f(x) and g(x). (4 marks) (b) For the following improper integral 27re3" dr (1) Identify the type of the integral; (4 marks) (ii) If convergent, find the value of the integral. (4 marks) (a) Consider the functions f, g : R → R defined by the expressions f(x) = 10a? + 60r – 50 and g(x) = 6x – x2. Find 40F 20 4. 20 40 10 (x2  6x+5) 100 (x6) x Figure 1: Plot of the two quadratics. (i) the area under f(r) and above y = 0; (2 marks) (ii) the area under g(x) and above y = 0; (2 marks) (ii) points ri < r2 where f(x) and g(1) intersect; (4 marks) (iv) the area between f(x) and g(x). (4 marks) (b) For the following improper integral 27re3" dr (1) Identify the type of the integral; (4 marks) (ii) If convergent, find the value of the integral. (4 marks)
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Related Book For
Introduction to Real Analysis
ISBN: 9780471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
Posted Date:
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