" समीकरण "(x^(2)+1)^(2)-x^(2)=0

(|x-2|-1)/(|x-2|-2)<=0

If alpha,beta are the roots of the equation x^(2)+x+1=0 , then the equation whose roots are alpha^(22)andbeta^(19) , is a) x^(2)-x+1=0 b) x^(2)+x+1=0 c) x^(2)+x-1=0 d) x^(2)-x-1=0

Let x=1+(1)/(1+(1)/(1+(1)/(1+(1)/(1+(1)/(1+alpha))))). Which of the following is correct? x^(2)+x+1=0 (b) x^(2)-x+1=0( c) x^(2)+x-1=0 (d) x^(2)-x-1=0

lim_(x rarr0)((5x^(2)+1)/(3x^(2)+1))^(1/x^(2))

lim_(x rarr0)((1+5x^(2))/(1+3x^(2)))^(1/x^(2))=

For x>0 Prove that x-(x^(2))/(2)

Solve each of the following initial value problems: (dy)/(dx)+(2x)/(x^(2)+1)y=(1)/((x^(2)+1)^(2)),y(0)=0( ii) (x^(2)+1)y'-2xy=(x^(4)+2x^(2)+1)cos x,y(0)=0

lim_ (x rarr0 ^ (+)) ((1- (cos (sin ^ (2) x)) / (x ^ (2))) ^ ((ta (1-2x ^ (2))) / (sin ^ (2) x))

lim_(x rarr0)([(2(cosh x-1))/(x^(2))]^(1))/(x^(2))