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

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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 :)

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  • $\begingroup$ 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! $\endgroup$ – Matti P. Nov 19 '19 at 11:13
  • $\begingroup$ @MattiP. It seems that the first one is continuous at $x=1$. $\endgroup$ – user Nov 19 '19 at 11:14
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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

$$\lim_{x\to 1} f(x)=f(1)$$

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