If `f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|, " then " f(3x) - f(x) =`

Evaluate |(x+lamda,x,x),(x,x+lamda,x),(x,x,x+lamda)|

Using Properties of determinants, prove that {:|(x+lamda,2x,2x),(2x,x+lamda,2x),(2x,2x,x+lamda)|=(5x+lamda)(lamda-x)^2

Evaluate the following determinant abs((x+lamda,x,x),(x,x+lamda,x),(x,x,x+lamda))

Evaluate the following: |[x+lamda, x, x],[x, x+lamda, x],[x, x, x+lamda]|

Evaluate the following: |[x+lamda, x, x],[x, x+lamda, x],[x, x, x+lamda]|

If f : R to R is defined by f(x) = {:{ ((cos 3x - cos x)/(x^(2) ), " for " x ne 0), (lamda , " for " x =0):} and if f is continuous at x =0 , then lamda is equal to