Calculus Answers

Using mean value theorem find the √11

Locate and classify the stationary points of the function

f( x,y ) x^2+y^2–6xy +6x +3y –4

Find the integral of f(x,y ) x^4+y^2 over the region bounded by y=x , y= 2x and x=2

Trace the curve y^3 = x^2 −1 , and state all the properties you use to trace it.

Trace the curve y^3 = x^2 −1 , and state all the properties you use to trace it.

Hi!
Help me please! I don't understand how determine an indefinite multiple integral. For instanse, \iint 1 dxdy = ?

(a)Calculate all the four second-order partial derivatives of the following functions:

(i) f(x,y)=cos(x^2+y^2)

(ii) f(x,y)=sin(x/y)


(b) Find the range of the function f defined by f(x,y) 10–x^2–y^2 for all (x,y)

for which x^2+y^2 ≤9 Sketch two of its level curves.

(c)Check whether the following functions are differentiable at the point given

against them:

(i)f(x,y)=|x=1|at (1,0)

(ii) f(x,y) =y^3+ ysin2x +e^(x+y) at (1,–1)


(d)Find dw/dt

w = xy + x,z = cos t, y = sint , z=1 at t= 0 .

(i)Find the integral of f(x,y ) x^4+y^2 over the region bounded by y=x , y= 2x and x=2

(ii)Find the surface area of the portion of the paraboloid z=25–x^2–y^2 which lies

above the xy -plane.

(iii)Locate and classify the stationary points of the function

f( x,y ) x^2+y^2–6xy +6x +3y –4

(iv)Check whether the following functions are homogeneous or not.

(a)x/y +3y/2x +sin√(x/y)

(b)x^4 +4x^2 +y^2)x^2


(v)Evaluate f(xy )at a point (x,y)for the function f defined by

f(x,y)=x^5 +10x^3 y^3 +8y^4

Verify that the function f satisfies the requirements of Schwarz’s theorem and

hence evaluate f(x,y)

How to solve a multivariable function using Lagrange multipliers

Trace the curve y =³√ x −1 , and state all the properties you use to trace it.