Prove that `underset(xrarr0)"lim"((1+x)^(n) - 1)/(x) = n`.

Prove that lim_(xrarr0) ((1+x)^(n) - 1)/(x) = n .

Prove that underset( n rarr oo)lim x_(n)=1, if x_(n)=(3^(n)+1)/3^(n) .

lim_(xrarr0) ((x+1)^(5)-1)/(x)

Evaluate lim_(xrarr0)((1+x)^(n)-1)/(x)

lim_(xrarr0)((1+x)^(n)-1)/(x) is equal to

Evalvate lim_(xrarr0)((1+x)^(4)-1)/(x).

Consider the following statements: I. underset(xrarr0)lim (x^(2))/(x) exists. II. ((x^(2))/(x)) is not continuous at x = 0. III. underset(xrarr0)(lim)(|x|)/(x) does not exist Which of the above statements are correct?

lim_(xrarr0) (sqrt(1+x+x^(2))-1)/(x)

Let f(x) = underset(n rarr oo)("Lim")( 2x^(2n) sin""(1)/(x) +x)/(1+x^(2n)) then find underset( x rarr -oo)("Lim") f(x)

Evaluate lim_(xrarr0) (1+x)^(1/x)