Evaluate the following: ` |[1,1,1],[1,1+x,1],[1,1,1+y]| `

Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

Evaluate the following: int_-1^1 (|x|+|x-1|)dx

Evaluate |[1,x, y],[1,x+y, y],[1,x,x+y]|

Prove that: |(1, 1, 1),( 1, 1+x,1) ,(1, 1, 1+y)|=x y .

Evaluate the following limits : Lim_(x to 1 ) (x-1)/(x+1)

Evaluate the following limits : Lim_( x to 1) x^(1/(x-1))

Evaluate the following limits : Lim_( xto 1) (x^(1//4)-1)/(x^(1//3) -1)

Evaluate the following: int_(-1//2)^(1//2)cos x "log" (1-x)/(1+x)dx

Find the value of the following: tan [1/2[sin^(-1) ((2x)/(1+x^2))+cos^(-1) ((1-y^2)/(1+y^2))]], |x| 0 and x y < 1 .

If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0 , then x^(-1)+y^(-1)+z^(-1) is equal to a.1 b.-1 c.-3 d. none of these