Evaluate the following limits `([dot],\ {dot}` denotes greatest integer function and fractional part respectively`)` `(lim)_(x->1)([x])/x`

Evaluate the following limits ([.],~ {.}~ denotes~ greatest integer function and fractional part respectively) (lim)_(x rarr1)([x])/(x)

Evaluate the following limits ([.],~ {.}~ denotes~ greatest integer function and fractional part respectively) (lim)_(x rarr1)(x)/([x])

Evaluate the following limits ([.], {.} denotes greatest integer function and fractional part respectively) lim_(x rarr1)x sgn(x-1)

Evaluate the following limits ([.],{.} denotes greatest integer function and fractional part respectively) lim_(x rarr0)an^(-1)(1)/(x)

Evaluate the following limits ([.],{.} denotes greatest integer function and fractional part respectively) lim_(x rarr0)(|x|)/(x)

Evaluate the following limits ([.],{.} denotes greatest integer function and fractional part respectively) lim_(x rarr0)(1)/(ln|x|)

Evaluate the following limits ([.],{.} denotes greatest integer function and fractional part respectively) lim_(x rarr0)cot^(-1)x^(2)

Evaluate the following limits ([.],~ {.}~ denotes~ greatest integer function and fractional part respectively) (lim)_(x rarr n)[x],(lim)_(x rarr n){x},n in I

Evaluate the following limits ([.],{.} denotes greatest integer function and fractional part respectively) limsin_(x rarr0)^(-1)[sec x]

Solve the equation [x]{x}=x, where [] and {} denote the greatest integer function and fractional part, respectively.