lim_(x rarr1)((1)/(x^(2)+x-2)-(x)/(x^(3)-1))

Evaluate the following limit : lim_(x rarr 1)(1/(x^2+x-2)-x/(x^3-1)) .

lim_(x rarr1)[(x-1)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+x)]

lim_(x rarr1)(x^(2)-2x+1)/(x^(2)-x)

lim_(x rarr1)((x^(4)+x^(2)+x+1)/(x^(2)-x+1))^((1-cos(x+1))/((x+1)^(2))) is equal to 1 (b) ((2)/(3))^((1)/(2))(c)((3)/(2))^((1)/(2))(d)e^((1)/(2))

Evaluate the following limits: (i) lim_(x rarr1)(x^(2)+3x+2)/(x^(2)+1)

lim_(x rarr1)(x^(2)-1)/(x-1)

lim_(x rarr1)(x^(2)-1)/(x-1)

lim_(x rarr1)(x^(3)-1)/(x-1)

lim_(x rarr1)(x^(2)+sqrt(x+3)-3)/(x^(2)-1)

prove that lim_(x rarr1)(x^(3)-1)/(x^(2)-1)=(3)/(2)