# Limit of function is a number from real numbers(not +- infinity)

I have to choose which functions(on graphs) have their own limit, a is only from real numbers(not +- infinity)

I think that their own limit have functions 1 and 4; number 3 does not exist and I am not sure about number 2.

Will you help me? thx a lot :)

• I would answer only the fourth one. The first one seens to go to $-\infty$; the second one is discontinuous; the third one goes to either $+\infty$ or $-\infty$ and the last one is even differentiable! – Matti P. Nov 19 '19 at 11:13
• @MattiP. It seems that the first one is continuous at $x=1$. – user Nov 19 '19 at 11:14

You are right, indeed both the second and the third options don't have limit for $$x \to 1$$ since right and left limits are different.
The first and the fourth one are continuous at $$x=1$$ and this guarantees that the limit exists since
$$\lim_{x\to 1} f(x)=f(1)$$