If `|{:(x+3,x+4,x+lambda),(x+4,x+5,x+mu),(x+5,x+6,x+v):}|=0` where `lambda,mu,v` are in A.P then prove that this is an identity in x.

Let A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}] then prove that A^(-1) exists if 3x+lambda ne0, lambda=ne0

Verify that the function y = 2lambda x + (mu)/(x) where lambda, mu are arbitary constants is a solution of the differential equation x^(2)y'' + xy' - y = 0 .

Let f(x)=lambda+mu|x|+nu|x|^(2), where lambda,mu,nu in R, then f'(0) exists if

If f(x) = {(x+lambda,",",x lt 3),(4,",",x = 3),(3x-5,",",x gt 1):} is continuous at x = 3, then lambda =

Prove that : |{:(x+a,x+2a,x+3a),(x+2a,x+3a,x+4a),(x+4a,x+5a,x+6a):}|=0

Let f(x)={(5^(1//x)"," , x lt 0),(lambda[x]",",x ge0):} and lambda in R , then at x = 0

If f(x)={:{([x]+[-x] , xne 0), ( lambda , x =0):} where [.] denotes the greatest function , then f(x) is continuous at x =0 , " for" lambda

If x(sgn x)(sgn x)+|x|(sgnx)^(3)=lambda x^(mu), then the value of lambda+mu is: