Evaluate :
`lim_( x -> 1 ) ( K^2/logx - K^2 /( x - 1 ))`

Evaluate lim_(x to 1) (x^3-1)/(x^2-1)

Evaluate: lim_(xtoe)(logx-1)/(x-e)

Evaluate: lim_(x rarr -1) (logx^(2)-log((1)/(x^(4)))+log3)/(log((x^(3))/(-3))) .

lim_(x->1)(1+logx-x)/(1-2x+x^2)

Evalaute lim_(xto1) (1+logx-x)/(1-2x+x^(2))

Evaluate lim_(xto1)(x^(3)-x^(2)logx+logx-1)/(x^(2)-1)

Evaluate lim_(x to 1) sum_(k=1)^(100) x^(k) - 100)/(x-1).

Evaluate the following limits : lim_(x to 1)(logx)/(x-1)

Evaluate: lim_ (n rarr oo) (1) / (n ^ (2)) sum_ (k = 0) ^ (n-1) [k int_ (k) ^ (k + 1) sqrt ((xk) (k + 1-x)) dx]

Evaluate: lim_(x rarr 1) [(logx^(3)+log((1)/(x^(2)))+log2)/(log(x^(3)+3))]