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5.(20%) Given the series ,(a) find the series' radius and interval of convergence. For what values of x does the series converge (b) absolutely,(c) conditionally?

其他申論題

3.(25%) Sketch the graphs of (You need to describe A: domain; B: intercepts; C: asymptotes(horizontal and vertical if any); D: intervals of increase and decrease; E: local maximum and minimum values; F: interval of concavity; G: point of inflection; H: sketch the curve)

6. (15%) Sketch the region of integration, and evaluate the integral.∫∫R xydA where R is the region bounded by the lines y=x,y =2x,and x+ y=2.

(a)∫x2exdx(10%)

(b) ∫xex^2dx (10%)

(d) ∫∫Dx + 2y dA, where D is the region bounded by the parabolas y = 2x2 and y = 1 + x2.(15%)

2. Please sketch the curve (You must describe the domain, intercepts, symmetry, asymptotes, increasing or decreasing, local maximum and minimum values, and concavity and points of inflection.) (15%)

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