Advanced Mathematics

Find the divergence of the vector 

Find the angle between any two diagonals of a cube.

Prove that the general equation of first degree in x, y, z represents a plane.

Find the angle between the lines,

Prove that the lines,

  are perpendicular 

Find the shortest distance between the lines.

Find the equation of the plane containing the point (2, 1, 1) and the line,

Find the constant 'a' so that the vectors  are co-planar.

If  and then prove that  is perpendicular to and also find

Find the volume of the parallelopiped whose co-terminal edges are represented by the vectors

 Find the velocity and acceleration of a particle moves along the curve  at any time t". 

Find the directional derivative of x²yz³ at(1, 1, 1) in the direction of 

Solve (D² + 2D + 1) = x² + 2x.

 show that 

Show that the vector field, is solenoidal.

Find the constants a, b, c such that the vector field,

Prove that L(sin at)= 

Find L[sint  sin 2t  sin 3t].

Find L[cos³t].

Find the inverse Laplace transform of 

Find 

Find 

Solve the differential equation,  under the condition  by Laplace transform techniques. 

Solve the differential equation,   by Laplace transform techniques.

Obtain reduction formula for  where n is positive integer.

Find the modulus and amplitude of 1 + cos+ i sin.

Find the cube root of 1 - i.

Find the n^th derivative of e^ax cos (bx+c).

Find the n^th derivative of 

If y= sin^_1 x, prove that 

Find the angle of intersection of the curves 

Find the nodal equation of the curve r (1-cos) - 2a.

Expand log (secx) upto the term containing x⁴ using Maclaurin's series.

If u = x³ - 3xy² + x + e^x cosy + 1₁ show that u_xx + t_yy = 0.

If prove that 

Find , where u = x+y+z, v= y + z ,w=z. 

Express the complex number

 in the form a + ib. 

Evaluate 

Evaluate 

Prove that: i) and    ii) (n+1) = n! for a positive integer n. 

Prove that 

Show that 

Solve 

Solve  dy = 0.

Solve  + y cotx =cosx.

Solved 

Solve (D² - 4D + 13)y = cos 2x.