Define Improper integral of Second kind and test the convergence of the integral
[3 marks]04 Define Gamma function. Prove that
[ marks]07 Obtain the Maclaurin’s series expansion of for . Using it, expand in powers of .
[ marks]03 Define Beta function. Show that
[ marks]04 Find local extreme value of the function
[ marks]Define geometric series and explain its convergence. Test the convergence for the following series.
[7 marks]Define nth term test for the divergence of a series. Test the convergence for the following series.
[7 marks]03 Evaluate :
[ marks]04 Find the area generated by revolving the curve
[ marks]07 Find radius and interval of convergence of the power series
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[3 marks]03 Evaluate :
[ marks]Find the volumes of the solids generated by revolving the region under the curve over the interval [1, 4] about the x-axis.
[4 marks]07 Define Alternating series. Verify whether the series is conditionally convergent or not.
[ marks]03 Evaluate the limit :
[ marks]04 Find Tangent plane and Normal line to the surface at the point (1,1,1) .
[ marks]Find the shortest and the longest distances of the point (1,1,1) from the sphere
[7 marks]03 Discuss the continuity of at the origin. where,
[ marks]04 Find the directional derivative of at the point (1, 0) in the direction of
[ marks]07 Find critical points of the function . Also find local maxima, local minima and saddle points, if any.
[ marks]03 Evaluate :
[ marks]04 Evaluate the integral over the region of the upper half of the circle
[ marks]07 Evaluate the integral by changing the order of the integral.
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[3 marks]03 Evaluate where Ris the region bounded by the parabolas and .
[ marks]04 Evaluate :
[ marks]07 Find the volume of the region bounded by a paraboloid , a plane and XY-plane. Page 3 of
[3 marks]