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

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.

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

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

If f(x)={(x^2+1,x>=1),(3x-1,x 1) f(x) is (a) 2 (b) - 2 (c) 1 (d) - 1

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

If f(x)=|[1,2(x-1),3(x-1)(x-2)],[x-1,(x-1)(x-2),(x-1)(x-2)(x-3)],[x,x(x-1),x(x-1)(x-2)]| . Then, the value of f(2020) is

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

Express the following in the lowest terms. ((2x^(2)+1)/(x-1)+(x-1)/(x+1))xx((x^(2)-1)/(2x)):