" *1."(x+4)/((x^(2)-4)(x+1))

If y=(1+(1)/(x^(2)))/(1-(1)/(x^(2)))backslash then (dy)/(dx)=-(4x)/((x^(2)-1)^(2))b-(4x)/(x^(2)-1) c.(1-x^(2))/(4x)d*(4x)/(x^(2)-1)

Prove that, (d)/(dx) ["log" (x^(2) + x + 1)/(x^(2) -x + 1) + (2)/(sqrt3) "tan"^(-1) (sqrt3x)/(1-x^(2))]= (4)/(x^(4 ) + x^(2) + 1)

Solve the inequality,(1)/(x-1)-(4)/(x-2)+(4)/(x-3)-(1)/(x-4)<(1)/(30)

int(x^(4)-1)/(x^(2)(x^(4)+x^(2)+1)^(1/2))dx" is equal to "

Evaluate: lim_(x rarr 1) (2x^(2)+4x+4)/(2x-1) .

lim_ (x rarr (1) / (2)) ((8x-3) / (2x-1) - (4x ^ (2) +1) / (4x ^ (2) -1))

lim_(x to 1/2)((8x-3)/(2x-1)-(4x^(2)+1)/(4x^(2)-1)) .

Lt_(x to oo)((8x-3)/(2x-1)-(4x^(2)+1)/(4x^(2)-1))=