137p_Assignment2_SOLUTIONS.pdf - MATH 137 Winter 2018...

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MATH 137 Winter 2018Assignment 2 – SOLUTIONS.1. Determine for which values ofxthe following series converge. Express your solution in the formx(a, b).i)Xn=1xnnii)Xn=114n(x+ 1)n,iii)Xn=1(-1)n+1xnnSOLUTIONS:
2. From the figure, determine the following limits, or explain why thelimit does not exist.SOLUTIONS:i)limx2+f(x) = 3,ii)limx→-3+f(x) = 0,iii)limx→-3-f(x) =-2,iv) limx4f(x) = 2,v) limx0f(x) =Does not exist,vi)limx2-f(x) =-∞Does not exist,vii)limx→∞f(x) = 4,viii)limx→-∞f(x) =-1,3.(a) Prove that there must exist at least one pointx=x?where the polynomialf(x) =x3+ax+bcrossesthex-axis,i.e.f(x?) = 0.

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