Supposing that you need to evaluate the limit `lim_(x-gtoo) sin((x-1)/(2+x^2)), ` hence you need to evaluate the sine of the limit of fraction `((x-1)/(2+x^2))` such that:

`lim_(x-gtoo) sin((x-1)/(2+x^2)) = sin lim_(x-gtoo)((x-1)/(2+x^2))`

You need to force x factor to numerator and `x^2` to denominator such that:

`sin lim_(x-gtoo)(x(1-1/x))/(x^2(2/x^2+1))`

`sin lim_(x-gtoo)((1-1/x))/(x(2/x^2+1)) = sin (1-0)/(oo(0+1))`

`sin lim_(x-gtoo)((1-1/x))/(x(2/x^2+1)) = sin (1/oo)`

lim_(x->oo) sin((x-1)/(2+x^2)) =

`sin lim_(x-gtoo)((1-1/x))/(x(2/x^2+1)) = sin 0`

`sin lim_(x-gtoo)((1-1/x))/(x(2/x^2+1)) = 0`

**Hence, evaluating the limit of the function `sin((x-1)/(2+x^2))` yields `lim_(x-gtoo) sin((x-1)/(2+x^2)) = 0` .**

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.