Q & A - Mathematics

Q & A

• Find Laplace inverse of 3s7 s 2 2s 3 Find Laplace inverse of (3s7)/(s^2-2s-3) >
• Find Laplace inverse of ss24 Find Laplace inverse of s/(s^2-4) >
• Find Laplace inverse of s2 s a 2 Find Laplace inverse of s^2/(s-a)^2 >
• Find Laplace inverse of s s a s b Find Laplace inverse of s/(sa)(sb) >
• Find Laplace inverse of s2 s 2 2s 2 Find Laplace inverse of (s-2)/(s^22s2) >
• Evaluate integral over z2 OF cos piz z1 Evaluate integral over |z|=2 OF cos piz/(z-1) >
• Evaluate integral over the circle z3 of sin piz2 cos piz2 z-1 2 z-2 Evaluate integral over the circle |z|=3 of (sin piz^2 cos piz^2)/(z-1)^2 (z-2) >
• Evaluate integral over circle z 2 of 1 z 2 1 Evaluate integral over circle |z|=2 of 1/(z^2-1) >
• Evaluate integral of e2z z21 where C is the circle Evaluate integral of e^(2z)/(z^21) where C is the circle |z|=1/2 >
• Evaluate integral over C of z4z22z5 dx where C is the circle z1i Evaluate integral over C of (z4)/(z^22z5) dx where C is the circle |z1-i| =2 >
• Find Laplace transform of sin 3t t23t2 Find Laplace transform of sin 3t (t^2-3t2) >
• Find Laplace transform of Lsint t23t2 Find Laplace transform of L{sint (t^2-3t2)} >
• Find Laplace of t e t sin3t Find Laplace of t e^(-t) sin3t >
• Find Laplace transform of t2 et cost Find Laplace transform of t^2 e^(-t) cost >
• Find Laplace transform of e5t tcost 2 Find Laplace transform of e^(-5t) (tcost)^2 >
• Find Laplace transform of eat ebt t Find Laplace transform of (e^(-at) - e^(-bt))/t >
• Find Laplace transform of 1cost t Find Laplace transform of (1-cost)/t >
• Find Laplace transform of e4t sin 6tt Find Laplace transform of e^(-4t) sin 6t/t >
• Find the Laplace transform of ft sint when 0tpi and 0 when pit2pi and Find the Laplace transform of f(t) = sint , when 0
• Find the fixed point under the transformation Find the fixed point under the transformation z = (6z-9)/z >
• Find the fixed point of w 6z9 z Find the fixed point of w = (6z-9)/z >
• Find the bilinear transformation which maps the point infty i 0 of the z plane into the Find the bilinear transformation which maps the point infty, i, 0 of the z plane into the 0, i, infty of the w plane. >
• Find the blinear transformation that maps the points z0 1 i into the points Find the blinear transformation that maps the points z=0, --1, i into the points w =1,0,infty respectively >
• Find Laplace transform of ft where ft sint 0pi Find Laplace transform of f(t) where f(t) = sint, 0pi >
• Expand fz z3zz2z2 a Laurent series valid for Expand f(z) = (z3)/z(z^2-z-2) a Laurent series valid for |z|
• Find the Laurent expansion of the function ez z1 2 in the neighbourhood of the singular point Hence find the residue of that pole Find the Laurent expansion of the function e^z/(z-1)^2 in the neighbourhood of the singular point. Hence find the residue of that pole. >
• Obtain the first four terms of the Laurent expansion of ez zz21 in ascending powers of x valid in Obtain the first four terms of the Laurent expansion of e^z / z(z^21) in ascending powers of x valid in 0
• Obtain Laurent series expansion of fz Obtain Laurent series expansion of f(z) = (7z-2)/z(z-2)(z1) in 1
• Find the Laurent series of fz ez z1 2 about z Find the Laurent series of f(z) = e^z/(z-1)^2 about z=1 >
• Calculate the curl of the vector F xyz i 3x2 y j xz2 y2zk at Calculate the curl of the vector F = xyz i 3x^2 y j (xz^2 -y^2z)k at (1,-1,1) >
• Find the directional derivative of phi Find the directional derivative of phi = x^2 yz4xz^2xyz at (1,2,3) in the direction of 2i j -k >
• Find surface integral F x2 zj yzk over the cube formed by x 1 1 y 11 and z Find surface integral F = x^2 i zj yzk over the cube formed by x = -1, 1, y = -1,1 and z = -1,1 >
• Solve the Differential equation D3 D25D3y 0 Solve the Differential equation (D^3 D^2-5D3)y =0 >
• The equation of bending of a strut is The equation of bending of a strut is EI d^2 y/dx^2 py =0 at x=0 , y =1 at x =1/2. Find y >
• Solve D211D28y 13 cosh 2x Solve (D^211D28)y = 13 cosh 2x >
• Solve D24D4 y 11e2x Solve (D^24D4) y = 11e^(-2x) >
• Solve D27D12 14e3 Solve (D^27D12) = 14e^(-3x) >
• x ev sec u y ey tan u find Jacobian and inverse jacobian x = e^v sec u, y = e^y tan u, find Jacobian and inverse jacobian. >
• An experiment consist of four volleyball games played by one team How could a coin be used to represent the experiment in a simulation How could the event in which the team wins all four games be An experiment consist of four volleyball games played by one team. How could a coin be used to represent the experiment in a simulation? How could the event in which the ...
• An experiment consists of selecting a package of five electrical sockets The probability that any one electrical socket is defective is 10 How could a table of random digits be used to represent An experiment consists of selecting a package of five electrical sockets. The probability that any one electrical socket is defective is 10%. How could a table of random ...
• Find integral of root of 1sin 2x dx Find integral of root of (1sin 2x) dx >
• Evaluate integral of sin inverse of Evaluate integral of sin inverse of (2x/(1x^2)) dx >
• If x a cos nt b sin nt find second derivative of x wrt t If x = a cos nt= b sin nt find second derivative of x wrt t. >
• Find the equation of the plane through intersection of the planes Find the equation of the plane through intersection of the planes 3x-y2z-4 = 0 and xyz-2=0 and the point (2,2,1) >
• Find the foot of the perpendicular from 027 on the line Find the foot of the perpendicular from (0,2,7) on the line (x2)/-1 = (y-1)/3 = )z-3)/-2 >
• Find the shortest distance between the lines whose vector equations are Find the shortest distance between the lines whose vector equations are r = (1-t)i(t-2)j(3-2t)k and r = (s1)i (2s-1) j -(2s1)k >
• Find the intervals in which the function f 48322 2 24 21 is strictly increasing or strictly decreasing Find the intervals in which the function f(x) = x^4-8x^322x^2-24x21 is strictly increasing or strictly decreasing >
• Find the values of x and y if the vectors a 3ixj k and b 2ijyk are mutually perpendicular vectors of equal magnitude Find the values of x and y if the vectors a = 3ixj-k and b = 2ijyk are mutually perpendicular vectors of equal magnitude. >
• Find a vector d perpendicular to both Find a vector d perpendicular to both irj2k and 3i-2j7k and also for a c = 2i-j4k, c.d. =18
• Evaluate integral pi6 to pi3 of 1rt tanx Evaluate integral pi/6 to pi/3 of 1rt tanx >