7. Consider the following integrals:IZ∞0exe2x+ 3dxIIZ1-1ex-1exdxIIIZ10e4x√e2x+ 1dxWhich of the integrals are improper?a. I onlyb. II onlyc. I and II onlyd. III onlye. I, II and IIIf. None of the above.
8. Consider the following sequences:Ian=cos 4n4nIIbn=4n32n+1IIIcn=(-2)nn2Which of the sequences converge?
9. Consider the following series:I∞Xn=1cos2nn2+ 1II∞Xn=14n32n+1III∞Xn=1n-1√n4+n-1Which of the series converge?
10. A particle moves clockwise around the circle(x-1)2+y2= 9starting at the point(4,0).What parametric questions represent its motion?
2Free ResponseFor problems 11-15, show all work and justify each step to receive full credit. Draw a box around your answers.11. (10 points) Evaluate the integrals:
a.Zxlnx dxYour answer: