Calculus Answers

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.

Take 10 figure logarithm to base 10 from x = 300 to x = 310 by unit increment. Calculate
the first derivative of log10 x when x = 310

The annual inventory cost of C for a manufacturer is given by

C = (2 000 000)/x + 500x


where x is the number of items that are ordered each item. Find C(200) and C ‘ (200), and interpret the result.

Evaluate the integral  +
/ 2
0
2 cos
1
p
dx
x
.