`lim_(x->0)1/(1-e^(1/ x))=`

(lim)_(x->0)[((1+x)^(1//x))/e]^(1//x)\ \

lim_(x->0) ((1+x)^(1/x)-e)/x is equal to

Evaluate: lim_(x->0)(e-(1+x)^(1/x))/x

Evaluate: lim_(x->0)(e-(1+x)^(1/x))/x

Evaluate: lim_(x->0)(e-(1+x)^(1/x))/x

Statement 1: (lim)_(x->0)[x]((e^(1//x)-1)/(e^(1//x)+1)) (where [.] represents greatest integer function) does not exist. Statement 2: (lim)_(x->0)((e^(1//x)-1)/(e^(1//x)+1)) does not exist. Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true; Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

Evaluate: lim_(x->0)(e^x-1-x)/(x^2)

If lim_(x to 0)x^((1)/(1-x))=e^(-1)

lim_(x rarr0)(1+e^(-(1)/(x)))/(1-e^(-(1)/(x))))

Using lim_(x to 0)(e^(x)-1)/(x)=1 , show that, lim_(x to 0)log_(e)(1+x)/(x)=1