Question Video: Finding the One-Sided Limit of a Function from Its Graph at a Point If the Limit Exists | Nagwa Question Video: Finding the One-Sided Limit of a Function from Its Graph at a Point If the Limit Exists | Nagwa

# Question Video: Finding the One-Sided Limit of a Function from Its Graph at a Point If the Limit Exists

Determine lim_(π₯ β β5βΊ) π(π₯).

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### Video Transcript

Determine the limit as π₯ tends to negative five from above of π of π₯.

We are given a graph of the function π of π₯. And we can see that at negative five, that seems to be an asymptote. And therefore, the function π of π₯ is undefined at π₯ equals negative five, but weβre looking for the limit as π₯ tends to negative five from above. The little plus sign tells us that weβre only considering values of π₯, which are greater than negative five. Weβre getting closer and closer to negative five from above.

Looking back to the graph, we can see that π of negative four is negative one. π of negative 4.5 appears to be negative two. And as π₯ gets closer and closer to negative five, always remaining however greater than negative five, we can see that the value of π of π₯ decreases.

And as there is an asymptote there, in fact it will continue to decrease without bound. So it will go past negative a million, then negative a billion, negative a trillion. Every real number will be passed.

So the limit as π₯ tends to negative five from above of π of π₯ canβt be any real number because as π₯ gets closer to negative five, eventually the value of π of π₯ will become smaller than any number you could name.

Another way of saying this, a shorthand for this is that the limit as π₯ tends to negative five from above of π of π₯ is equal to negative infinity. This doesnβt mean that negative infinity is being considered as a number; this is just a shorthand for the statement we talked about before, which is that as π₯ gets closer and closer to negative five from above, π of π₯ decreases without bound.

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