|[x^(2)-x+1,x-1],[x+1,x+1]|

(i) {:[( cos theta , -sin theta ),( sin theta , cos theta ) ]:}" " (ii) {:[( x^(2) -x+1,x-1),( x+1,x+1) ]:}

(i) {:[( cos theta , -sin theta ),( sin theta , cos theta ) ]:}" " (ii) {:[( x^(2) -x+1,x-1),( x+1,x+1) ]:}

Find the value of the determinants (i) {:[( cos theta , -sin theta ),( sin theta , cos theta ) ]:}" " (ii) {:[( x^(2) -x+1,x-1),( x+1,x+1) ]:}

Evaluate the determinants (i) {:[( cos theta , -sin theta ),( sin theta , cos theta ) ]:}" " (ii) {:[( x^(2) -x+1,x-1),( x+1,x+1) ]:}

[[3x^(2),3x,1x^(2)+2x,2x+1,12x+1,x+2,1]]=(x-1)^(3)

Evaluate the determinants in (i) |costheta-sinthetasinthetacostheta| (ii) |x^2-x+1x-1x+1x+1|

Find lim_(xrarr1) f(x) where f(x)= {[(x^2-1)/(x-1), x ne 1],[1, x=1]:}

The constant term in the expansion of |(3x +1,2x-1,x+2),( 5x-1, 3x+2,x+1),(7x-1,3x+1,4x-1)| is

Let y=sqrt(2/(x^(2)-x+1)-1/(x+1)-(2x+1)/(x^(3)+1)) , find all the real values of x for which y takes real values.

For what value of k is the function f(x)={(x^2-1)/(x-1), ,x!=1,k,x=1" continuous at"x=1?