`lim_(x to 1) [x/(x-1)-1/logx]`

lim_{x \to 1} (3x)/(x-1)

Evaluate : lim_(x to -1) x/([x])

(i) lim_(x to 0) (a^(x) - 1)/(log_(a)(1 + x)), a gt 0 (ii) lim__(x to 0) (In (X + a)- In a)/(e^(2x) - 1) (ii) lim_(x to (pi)/(4)) (In(tanx))/(1 - cotx)

Evaluate the following limits : Lim_(x to 1 ) (x-1)/(x+1)

lim_(x to -1) ((1)/(x)+1)/(x+1)

Evaluate lim_(x to 1) (x^(3) - 1)/(x - 1)

Evaluate : lim_(x to 1) (x^(m)-1)/(x^(n)-1)

Evaluate the following limits : Lim_(x to 1) (x^(2) - x log x + log x - 1)/(x-1)

lim_(x to 0) (cos 2x-1)/(cos x-1)

lim_(x to 0) (x)/(sqrt(1+x-1))