`|(x^(2)-x+1, x-1),(x+1,x+1)|`

Find the domain of the following functions: f(x)=sqrt(((2)/(x^(2)-x+1)-(1)/(x+1)-(2x-1)/(x^(3)+1)))

Nurmber of non negative integral values of x satisfying the inequality (2)/(x^(2)-x+1)-(1)/(x-1)-(2x-1)/(x^(3)+1)>=0 is

Let f(x) denote the departement f(x)=|{:(x^2,2x,1+x^2),(x^2+1,x+1,1),(x,-1,x-1):}| on expansion f(x) is sen to be a 4th degree polynomial given by f(x)=a_0x^4+a_1x^3+a_2x^2+a_3x+a_4 Using defferentiation of otherwise, match the values of the uantities on the left to those on the right.

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

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.

f(x) = {((2x+1), x lt 1),(2,x=1),(x^(2)+1, x gt 1):} is

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

Discuss the continuity of the function f(x) ={(1+x^2,x le 1),(1-x, x gt 1):} at x=1.