Which of the following true ({.} denotes the fractional part of the function)? `("lim")_(xvecoo)((log)_e x)/({x})=oo` (b) `("lim")_(xvec2^+)x/(x^2-x-2)=oo` `("lim")_(xvec1^-)x/(x^2-x-2)=-oo` (d) `("lim")_(xvecoo)((log)_(0.5) x)/({x})=oo`

lim_(x rarr oo)((log x)/(x^(n)))

lim_(x rarr oo)((log x)/(x))^(1/x)

lim_(x rarr oo)(log(1+x))/(x)

lim_(x rarr oo){((log x)^(3))/(x)}

Evaluate: ("lim")_(xvec2)(x-2)/((log)_a(x-1))

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

lim_(x->oo) (x-sqrt(x^2+x))

Which of the following is and determinate form (lim)_(xvec1)(x^3-1)/(x-1) b. (lim)_(xvec0)(1+x)^(1//x) c. (lim)_(xvec1)(1/(x^2-1)-1/(x-1)) d. (lim)_(xvec0)(|x|)^(s in R)

lim_(x->oo ){(e^x+pi^x)^(1/x)}= where {.} denotes the fractional part of x is equal to

Given a real-valued function f such that f(x)={(tan^2{x})/((x^2-[x]^2) sqrt({x}cot{x}),for x 0 Where [x] is the integral part and {x} is the fractional part of x , then ("lim")_(xvec0^+)f(x)=1 , ("lim")_(xvec0^-)f(x)=cot1 , cot^(-1)(("lim")_(xvec0^-)f(x))^2=1 , tan^(-1)(("lim")_(xvec0^+)f(x))=pi/4