5 let f be the function whose graph is shown below evaluate...

5. Let $f$ be the function whose graph is shown below. Evaluate the limits using the graph. (a) $\lim_{x \to 0^+} f(x)$ (b) $\lim_{x \to 1^-} f(x)$ (c) $\lim_{x \to 2^+} f(x)$ (d) $\lim_{x \to 2^-} f(x)$ (e) $\lim_{x \to 3^-} f(x)$ (f) $\lim_{x \to 3^+} f(x)$ (g) $\lim_{x \to 4^+} f(x)$ (h) $\lim_{x \to 4^-} f(x)$ (i) $\lim_{x \to 5^-} f(x)$ (j) $\lim_{x \to 5^+} f(x)$

Transcript

00:01 All right, let's go ahead and answer this question.

00:04 For those who are reviewing how limits work, this is actually a very good practice problem.

00:13 So i really recommend you to go through this in detail if you're really struggling with these kind of questions.

00:19 Okay.

00:20 All right, so let's go through it.

00:22 It's asking you, you have the function f of x and the limit as x approaching to these number, or infinity, negative infinity, zero, et cetera, they're asking what the limit is going to be.

00:36 So long story short, the behavior of the graph is basically what limits are asking you to do.

00:46 So let's start with the first one.

00:49 The limit as x is approaching to 1.

00:52 So as x gets closer and closer to 1 from the negative and the positive direction, you can see that the y values are actually approaching to this circle right here at one comma one so we simply say that all right as x approaches to one y approaches to one as well so the answer is going to be one okay now what is happening as x is approaching to two now from the left side you can see that the y value is getting close to two but from the right direction, you are actually approaching to 1.

01:35 So because 2 and 1 are not the same thing, that is a situation where we know that it's undefined.

01:44 So this one doesn't have any good answer.

01:47 Number, when x is approaching 3, from the left side, we can see that it's approaching to 2.

01:57 From the right side, it's approaching to zero.

02:02 So for the same reason as two, we know that it's undefined.

02:06 Further, what we can say is that f of 3 itself is actually located at 1.

02:13 So that could have been a question that i would have asked, okay, if i were teaching this course.

02:20 Now, if x is approaching to 4, oh, sorry, i didn't include that in the graph, 4, you can see that it's approaching to this number.

02:30 Now regardless of the fact that it's a corner right there, it's still continuous.

02:36 It's still connected.

02:38 So from the left side, you know that it's approaching to a height of one.

02:44 From the right side, it's also approaching to the point one.

02:48 So we know that the answer is going to be one...

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