`lim_(x->1)[(x+2)/(x^2-5x+4)+(x-4)/(3(x^2-3x+2))]`

lim_(x rarr 1) [(x+2)/(x^2-5x+4)+(x-4)/(3(x^2-3x+2))]

lim_(x rarr1)[(x+2)/(x^(2)-5x+4)+(x-4)/(3(x^(2)-3x+2))]

Evaluate: lim_(x->oo)((x^2+x-1)/(3x^2+2x+4))^((3x^2+x)/(x-2))

lim_(x to 1)(x^(2)-6x+5)/(x^(2)+3x-4)=

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

lim_(x to 1) (x^4+4x^3-5x^2)/(x-1)

lim_(x->1)(x^4-3x^2+2)/(x^3-5x^2+3x+1)

Find the limits (i) (lim)_(x->1)[(x^2+1)/(x+100)] (ii) (lim)_(x->2)[(x^3-4x^2+4x)/(x^2-4)]

lim_(x=1)[(pi cot pi x)/(x)+(3x^(2)-1)/(x^(2)-x^(4))]

Which of the following is/are true? (a) lim_(x->oo)((2+x)^(40)(4+x)^5)/((2-x)^(45))=1 (b) lim_(x->0)(1-cos^3x)/(xsinxcosx)=3/2 (c) lim_(x->0)(ln(1+2x)-2"ln"(1+x))/(x^2)=-1 (d) lim_(x->oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(sec^1((2x+1)/(x-1)^2)=1