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11756_HW 3 MTH141 - 6 7 2 2 3 xy x y x in powers of(x-2...

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LOVELY PROFESSIONAL UNIVERSITY HOME WORK: 3 School: Department: Mathematics Name of the faculty member: Vinay Course No: MTH 141 Course Title: ENGINEERING MATHEMATICS-1 Class: Term: I Section: Batch: 2010 Max. Marks: 18+7=25 Date of Allotment: Date of Submission: Part-A Q. 1 Find the equation of tangent plane and the normal to the surface (a) ) 1 ( 4 2 2 2 y x z + + = at (1,0,6) (b) 1 25 9 4 2 2 2 = - + z y x at (2,3.4) Q. 2 Find the angle between the two surfaces 2 2 2 2 3 2 & y x z y x z - = + = at (2,1,5) 3 (a) Expand y e x sin in the powers of x and y as for as terms of third degree. (b) Using Taylor’s theorem to express the polynomial
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Unformatted text preview: 6 7 2 2 3 + + + xy x y x in powers of (x-2) an (y-1) Part-B Q. 4 Discuss the maxima and minima of the function 12 6 2 2 + + + x y x Q5 Test the following surface for maxima, minima and saddle points xy x x x z 6 3 2 6 2 3 2 + +-= Q 6 (a) Find the extrema of f(x,y)= ( 29 2 2 6 2 2 x x e y x + + (b) Evaluate the following integral ∫∫ 2 1 3 1 2 dxdy xy Date: Sig. of Faculty member Remarks by HOD (Mandatory) Sig. of HOD with date Remarks by HOS (Mandatory) Sig. of HOS with date...
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