Evaluating limits (Absolute values and trigonometric funtions)

[Absolutism]

Homework Statement

So, the question is about evaluating limit of the equations given. The right and left hand sides should be found so that we can see if the limit exists or not. I am not sure how to write this in, but basically they're like both put in a big "{" so, i'll write both with an "and" in between

Homework Equations

f(x) = (x/lxl)-3sinx/x , if x>0
and
( x-1/lx-1l) + 7x^2-1, if x<0
Find the limit of f(x) when X approaches 0, if it exists

The Attempt at a Solution

for the first equation, I believe we should first simply the term with a "sin" , so the result is 4 because sinx/x is 1 and then 1+3=4? I am not sure how to get the limit with this modulus in the denominator. X approaches zero from the right side for example. Is that a positive infinity, and so on?
For the second one it's basically the same issue, except, I am not very sure what to do with the rest of the terms outside.
generally, should I get the right hand side and left hand side for each equation? should then the four answers be equal?

 

[Trevor Vadas]

I think your on the right track. For the part where x>0 you should look at it as x goes to 0 from the right. Then for the part where x<0 look as the limit as x goes to 0 from the left. then the limit exists if those are equal.

 

[Absolutism]

I think your on the right track. For the part where x>0 you should look at it as x goes to 0 from the right. Then for the part where x<0 look as the limit as x goes to 0 from the left. then the limit exists if those are equal.

So, if x approaches to zero for example, from the left hand side, I should substitute in the equation by a negative number, and then a positive one if x approaches from the right?