`lim_(x rarr oo)Sin(1/x)`

lim_(x rarr oo)x sin(1/x)=

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

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

lim_(x rarr oo) tan(1/x)/(1/x)

lim_(x rarr oo)(x-1)/(x)

lim_(x rarr oo)(1)/(x)=0

Statement 1:f(x)=((x-1)(x-2))/((x-3)(x-4)), then lim_(x rarr oo)sin^(-1)f(x) exists,but lim_(x rarr oo)cos^(-1)f(x) does not exist.Statement 2:sin^(-1)x and cos^(-1)x are defined for x in[-1,1].

Evaluate the following limit: lim_(x rarr oo)(sin(a+x)+sin(a-x)-2sin a)/(x sin x))

Evaluate the following limit: lim_(x rarr oo)(sin(a+x)+sin(a-x)-2sin a)/(x sin x))

lim_(x rarr oo)(1)/(x^(2))