Which of the following limits vanishes ? `lim_(x->0)(1/x-1/(tanx))`

Which of the following limits vanishes? lim_(x rarr0)((1)/(x)-(1)/(tan x))

Which of the following limits vanish? lim_(x rarr oo)(sin x)/(x)

Which of the following limits vanish (A) Lim it_(x rarr oo)x^((1)/(4))sin((1)/(sqrt(x)))

Which of the following limits does not exist ?(a) lim_(x->oo) cosec^(-1) (x/(x+7) (B) lim_(x->1) sec^(-1) (sin^(-1)x) (C) lim_(x->0^+) x^(1/x) (D) lim_(x->0) (tan(pi/8+x))^(cotx)

Evaluate the following limits: lim_(xrarr0)((2^(x)-1)/(x))

Evaluate the following limit: (lim)_(x->0)(e^(tanx)-1)/x

Evaluate the following limit (lim)_(x->pi/2)(sin x)^(tanx)

Evaluate the following limit: (lim)_(x->0)(2x-s in x)/(tanx+x)

Which of the following limits tends to unity? (a) ("lim")_(xvec0)sin(tanx)/(sinx) (b) ("lim")_(xvecpi/2)sin(cosx)/(cosx) (c) ("lim")_(xvec0)"sin"(e^x-1)/x (d) ("lim")_(xvec0)(sqrt(1+x)-sqrt(1-x))/x

Which of the following limits tends to unity? (a) ("lim")_(xvec0)sin(tanx)/(sinx) (b) ("lim")_(xvecpi/2)sin(cosx)/(cosx) ("lim")_(xvec0)"sin"(e^x-1)/x (d) ("lim")_(xvec0)(sqrt(1+x)-sqrt(1-x))/x