Expand x+2y+1 in powers of (x-1) and (y-2) upto second degree terms by applying the Taylor's...

 

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Expand x²+2y²+1 in powers of (x-1) and (y-2) upto second degree terms by applying the Taylor's theorem. Q.2 Find the Taylor series expansion of es at (1,1) in powers of x and y upto second degree. Q.3 If f(x,y)-tan-xy. Find an approximate value of f(1.1,0.8) using the Taylor's series (i) linear approximation (ii) quadratic approximation. Q.4 Find the equation of tangent plane to√x²+1+1 at (-4,3). Q.5 The diameter and altitude of a right circular cylinder are measured as 4 cm and 6 cm respectively. If the possible error in each measurement is 0.1 cm. Find approximately the maximum possible error in the value computed for the volume and lateral surface. 115 Q.6 Find the value of [(3.82)²+2(2.1)] using theory of approximation Q.7 Find the extrema of f(x,y)=x²+xy +y²+x-1+y-1 Q.8 Examine the function f(x,y)-x+3xy-15x-15y+72x for extreme values. Q.9 Find the volume of the greatest rectangular parallelopiped inscribed in the ellipsoid whose equation is Q. 10 Find the shortest distance from origin to the surface xyz=2 Q.11 Find the maximum and minimum values of the function (x-3)+(y-4)+(z-12) subject to the condition x²+y2+22=1. Q. 12 A rectangular box open at the top, is to have a volume 32 cm³, find the dimension of the box requiring least material for its construction. Expand x²+2y²+1 in powers of (x-1) and (y-2) upto second degree terms by applying the Taylor's theorem. Q.2 Find the Taylor series expansion of es at (1,1) in powers of x and y upto second degree. Q.3 If f(x,y)-tan-xy. Find an approximate value of f(1.1,0.8) using the Taylor's series (i) linear approximation (ii) quadratic approximation. Q.4 Find the equation of tangent plane to√x²+1+1 at (-4,3). Q.5 The diameter and altitude of a right circular cylinder are measured as 4 cm and 6 cm respectively. If the possible error in each measurement is 0.1 cm. Find approximately the maximum possible error in the value computed for the volume and lateral surface. 115 Q.6 Find the value of [(3.82)²+2(2.1)] using theory of approximation Q.7 Find the extrema of f(x,y)=x²+xy +y²+x-1+y-1 Q.8 Examine the function f(x,y)-x+3xy-15x-15y+72x for extreme values. Q.9 Find the volume of the greatest rectangular parallelopiped inscribed in the ellipsoid whose equation is Q. 10 Find the shortest distance from origin to the surface xyz=2 Q.11 Find the maximum and minimum values of the function (x-3)+(y-4)+(z-12) subject to the condition x²+y2+22=1. Q. 12 A rectangular box open at the top, is to have a volume 32 cm³, find the dimension of the box requiring least material for its construction.

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To expand fx y x 2y 1 in powers of x 1 and y 2 up to seconddegree terms using Taylors theorem well f... View the full answer