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Find the second Taylor polynomial of f(x,y)=1+3x^2y-4y^3 at (1,1).
Near what points may the surface x^3+3y^2+8xz^2-3z^3y=1 be represented as a graph of a differentiable function z= k(x,y)? Justify your answer.
Find the points ( x,y) on the unit circle, at which the product xy is maximum or minimum
If f(x,y)= x^1/4+y^1/4/x^1/5+y^1/5,then show that x×∂f/∂x+y×∂f/∂y=1/20×f(x,y)stating the results used.
If f(x,y,z)= (coax,siny,tanz) and g(x,y,z)=(x-3,y^2-1,z^2-1), then find fog.
Find the derivative of f(x) = e^xlnx+x^2 using the concept of total derivative.
Using polar coordinates, show that lim x→0 y→0 x^3-y^3/x^2+y^2 =0.Also, find the two repeated limits.
let f(x,y)={ xy^5/x^2+y^4 where (x,y) is not equal to (0,0) and 0 where (x,y) = 0
Math
a) Find the values of aÎR for which a i is a solution of z 2z 7z 4z 10 0 4 3 2 − + − + = .
Also find all the roots of this equation. (5)
b) Find all the 8th roots of 3i − 3. Also show any one of them in an Argand diagram.
Also find all the roots of this equation. (5)
b) Find all the 8th roots of 3i − 3. Also show any one of them in an Argand diagram.
Math
Obtain the resolvent cubics, by Descartes’ method and by Ferrari’s method, of the
equation x 4x 8 0 4 3 + + = . Are the cubics the same? Further, use either method to
obtain the roots of this equation.
equation x 4x 8 0 4 3 + + = . Are the cubics the same? Further, use either method to
obtain the roots of this equation.
