Math Answers

if z=e^(xy^2),x=tcost,y=tsint then find dz/dt when t=π/2.

If f(x,y)=x^2tan^-1(y/x)y^2tan^-1(x/y)[xnot=0,y not=0]
=0(x=0=y)
then show that
(Partial d^2f)/(partial dx *partial day)=(x^2-y^2)/(x^2+y^2)

Evaluate the integral by converting to polar coordinates

INTEGRAL SIGN(0to √3) INTEGRAL SIGN (y to√(4-y^2))[dxdy/4+x^2+y^2]

If possible then find the value of f such that

F=(4x^3+9x^2y^2,6x^3y+6y^5)=∇f

Find the value of a,b and c such that

lim xtend to infinity(ae^x-bcosx+ce^-x)/xsinx=3/2

Solve the PDE
1.(D^2+D-1)z=4e^(x+y) cos(x+y)

Verified that the equations
1.z=root(
2x+a)+root(2y+b) and
2.z^2+meu=2(1+lemda^-1)(x+lemda y)

are both complete integrals of the PDE z=1/p+1/q.Also show that the complete integral (2)is the envelope of the one parameter sub-system obtained by taking b=-a/lemda-meu/(1+lemda) in the solution (1)

A random variable X has following probability distribution :- f(x)={cx^2 for 0<x<3 otherwise 0.determine the value of c and var(x).

The waveform of a voltage in an electrical circuit has the following parameters:
 A continuous series of right-angled triangles, each with a base length equivalent to 3 ms, 9 V maximum
-Voltage ramps up over the 3 ms and then drops back to zero instantaneously
-Sketch the waveform and mark on the relevant parameters.
-Derive the function which defines the waveform.
-Using integral calculus, find the RMS value of the voltage.
The acceleration of a sliding component in a packaging machine is given by the following expression: (d^2 s)/(dt^2 ) =12t+3

Obtain the curl of the following vector field:rA = ( eˆ r + r c o s θ eˆ θ + r eˆ φ )