# midterm4.pdf - Question 1(6 points A curve is given by the...

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Question 1.(6 points)A curve is given by the parametric equationsx=et+ 1,y= 2t-3.Eliminate the parameter to find a Cartesian equation for the curve.Question 2.(6 points)Find the equation of the tangent line to the following curve at (0,2)x= ln(t),y= 1 +t2.Page 2
Question 3.(6 points)Set up an integral to find the length of the curve given by parametric equationsx=t+pt,y=t-pt,0t1.Question 4.(8 points)Find the radius and interval of convergence of the power series1Xn=1n(2x-1)n4nRadius of convergence:Interval of convergence:Page 3
Question 5.(14 points)Recall that a series is said to beconditionally convergentif it is convergent but not absolutelyconvergent.Determine whether the following series are absolutely convergent, conditionally convergentor divergent.[Hint: you may find useful the fact thatlimn!11 +1nn=e.](a)1Xn=2(-1)nn+ 1nn2(b)1Xn=2cos(n+ 1)npn2-1Page 4
Question 6.(18 points)Consider the power seriesf(x) =1Xn=1xnn.