Find the Taylor series generated by the function f(x)=1x2 at x=1.a. Find the area of the region in the xy-plane enclosed by the curve r=1-cos.b. Find the length of this curve.c. Graph this curve in the Cartesian xy-plane.Use the Integral test to determine whether the series n=11n(1+ln2n) is convergent or divergent.Use the Integral test to determine whether the series n=1n1n(1+ln2n) is convergent or divergent.Let x=1+et and y=1-e'. Find the value of d2ydx2 at t=0.Consider the curve parametrized by x=2t2+3 and y=t4.a. Find an equation for the line tangent to the curve when t=-1.b. Calculate d2ydx2 at t=1.a. Find a power series representation for the function f(x)=xarctanx.b. Find the radius and the interval convergence of the series x=1(2x-3)n3**n.Let I:n=1n22n2+1,II:n=1n3(2n-1)!, and III:n=11(n2+1)n. Then,a) I converges, ?I diverges, III converges.b) I diverges, II converges, III diverges.c) I diverges, II converges, III converges.d) I converges, I? converges, III diverges.e) I diverges, II diverges, III diverges.01dx1-x22 is equal toa)4b)6c)2d)e)54Let an=8n+10**6n+12n. Then limnan is equal toa)45b)1c)56d)e)0The sum of the series n=02n+37** is equal toa)710b)825c)1450d)565e)3235The interval of convergence of the series n=1n(x+1)n2n isa)(-3,1)b)-3,1c)[-3,1)d)(-3,1]e)(-,)Which of the following can not be said about the series n=1(-1)n-12n+1?a) It is convergent.b) It converges absolutely.c) It converges conditionally.d) It is divergent.e) It is neither convergent nor divergent.01dx1-x22 is equal toa)4b)6c)2d)e)54The Cartesian equation of the curve whose polar coordinate is r=4tansec equalsa)xy=4b)x2=4xyc)x2y=4d)x2=4ye)y2=4x-22dxx2+4 is equal toa)34b)3c)4d)2e)56Which of the following pairs of polar coordinates does not label the same points?a)(2,73),(-2,-23)b)(-r,+),(r,)c)(2,0),(-2,)