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 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 (x) = 0 is continuous when f(x) ={((1-cos Ay)/(y sin y)),(1/2):}, ((y ne 0),(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 values of 'x' and 'y' from the following matrix equation: {:[(2x+1), 2y),(0,y^2-5y)] = [(x+3, y^2+2),(0,-6)]

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

Find the greatest value of x^3y^4 if 2x + 3y = 7 and x>=0,y>=0 .

Find the particular solution of the differential equation cos x (dy/dx) = y sin x, y = 1 when x = 0 .

If y = sin^-1((sinalpha sin x)/(1-cos alpha sinx)) , find y'(0)