If `A=[(x,x),(x,x)]` then `A^n =............`and `n epsilon N`

If A=([x,x],[x,x]) then A^(n)(n in N)= 1) ([2^nx^n,2^nx^n],[2^nx^n,2^nx^n]) 2) ([2^(n-1) x^n,2^(n-1) x^n],[2^(n-1) x^n,2^(n-1) x^n]) 3) I 4) ([2^(n) x^(n-1),2^(n) x^(n-1)],[2^(n) x^(n-1),2^(n) x^(n-1)])

If A={x:x=3n,n epsilon Z} and B={x:x=4n,n epsilon Z} , then find A nn B .

If A={x:x=3n,n epsilon Z} and B={x:x=4n,n epsilon Z} , then find ( A nn B ).

Properties of smallest integer function property (i)[-n]=-[n]where n epsilon N (ii) [-x]=-[x]+1; where xepsilon R-Z (iii) [x+n]=[x]+n where x epsilon R-Z and n epsilon Z (iv) [x]+[-x]={1; x notinZ ; 0 ; xinZ} (v) [x]-[-x]={2[x]-1; xnotinZ ; 2[x] ; if xinZ

If A ={(x,y): y=e^(x), x epsilon R} and B={(x,y):y=e^(-x), x epsilon R) then n(AcapB) is _________

If X={8^n-7n-1:n epsilon N} and Y={49(n-1):n epsilon N} , then

Simplify (1 + cos x + i sin x)^n, n epsilon N.

If lim(n->oo)(n*3^n)/(n(x-2)^n +n*3^(n+1)-3^n) = 1/3 then the range of x is (where n epsilon N )