Calculus Answers

Find fog and gof ,if they exist , for the functions f(t)=4t , t€R , g(x,y)= x + y, x,t€R.

Find the point on the ellipse x^2/4 +y^2 =1, that is nearest to the origin.

Find the slopes of the tangents to the curves of intersections of the planes x=0, y=2 and the surface z= x^3 + e^yx at the point (0,2,1).

y= (x-2)(x+1)

find two level curves of the function f(x,y)= (x+y)/(x-y) , x is not equal to y and sketch them

Evaluate the integral by converting to polar coordinate intergrate 0 to √3 double integrate y to√(4-y^2) dx.dy/(4+ x^2+y^2)

obtain all the first and second order partial derivatives of the function:
f(x,y)=sinxy

Evaluate the integral by converting to polar coordinate intergrate 0 to √3 double integrate y to√(4-y^2) dx.dy/(4+ x^2+y^2)

check whether there exists a continuously differentiable function g defined by f(x,y) =0 in the neighbourhood of x=3 such that g(3) =1/3 .

Check whether the function f : R2 to R defined by f(x,y)=2x^4 -3x^2y +y^2 has an extrema at(0,0).