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MAD 1181 / I Semester / Module IV, Differential calculus of several variables, PART A:, Find the Taylor’s series of near the point upto the first degree., If and find ., State Taylor’s series for two variables., The transformation of Cartesian co-ordinates to polar co-ordinates is given by . Find its Jacobians., State the conditions for maxima and minima for the functions of several variables., Define saddle point., If prove that, Find when ., Find dy/dx if through partial differentiation., Expand in powers of and upto terms of first degree., PART B:, Find, Find, Find, Find, Expand in powers of and using Taylor’s Expansion., Expand in powers of and using Taylor’s Expansion., Obtain terms upto third degree in the Taylor’s series expansion of near the point, Obtain terms up to third degree in the Taylor’s series expansion of near the point, Find the extreme values of ., Examine for its extreme values., Find the extreme points of ., Find the maximum and minimum values of ., Find the greatest rectangle inscribed in an ellipse., Use Lagrange’s multiplier to find the point of the plane which is nearest to the origin., If and , verify that, Find the Jacobian if ,