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)`

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

Evaluate the following limits, if they exist : lim_(x to 3)[x(x+1)]

lim_(x to 0) tan^-1x/x

Evaluate the following limits : Lim_(xto oo) x tan (1/x)

lim_(x rarr oo)sec^(-1)((x)/(x+1)) is equal to:

Evaluate the following limits : Lim_(x to 0) (3^(x)-1)/x

Which of the following is/are true? (a) lim_(x rarr oo)((2+x)^(40)(4+x)^(5))/((2-x)^(45))=1(b)lim_(x rarr0)(1-cos^(3)x)/(x sin x cos x)=(3)/(2)(c)lim_(x rarr0)(ln(1+2x)-2ln(1+x))/(cot^(-1)(sqrt(x+1)-sqrt(x)))=-1 (d) lim_(x rarr oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(sec^(1)((2x+1)/((x-1)^(2)))=1)=-1 (d)

Lim_(x to pi) (1+sec^(3)x)/(tan^(2)x)

Evaluate the following limits: lim_(x to 0)(sin^(-1)x-tan^(-1)x)/(x^(3))