Find the value of A ' if the function 'f' at z = 0 is continuous when `f(x)= {((1-cos z)/(Az sin z),,z,ne,0),(1/2,,z,=,0):}`

Find the value of A ' if the function 'f' at y = 0 is continuous when f(x)= {((1-cos y)/(y sin y),,y,ne,0),((1/2)A,,y,=,0):}

Find the value of 'A', if the function f at (x) = 0 is continuous when f(x) ={((1-cos Ax)/(x sin x)),(1/2):}, ((x ne 0),(x =0))

Find the value of 'A', if the function f at (x) = 0 is continuous when f(x) ={((1-cos Ay)/(y sin y)),(1/2):}, ((y ne 0),(y =0))

Find the values of x,y,z and w from the following equation : [(x-y,2x+z), (2x-y, 3z+w)] = [(-1,5),(0,13)]

Find the number of integral solutions of equation x+y+z+t=29, when x >= 1, y >= 2, z>=3 and t >= 0

Find the values of x, y, z if the matrix A = [[0,2y,z],[x,y,-z],[x,-y,z]] satisfy the equation A'A = I

Show that the following function is continuous at x = 0: f(x) = x sin1.x, when x ne 0 f(0) = 0.

Find the equation of the image of the plane x-2y+2z-3=0 in plane x+y+z-1=0.

Show that for z in C, |z|=0 if and only if z=0.

Let y=f(x) be a differentiable function AA x in R and satisfies: f(x)=x+int_(0)^(1)x^(2)zf(z)dz+int_(0)^(1)xz^(2)f(z)dz.