The graph of f is given. Use the graph to compute the quantities asked for, if a = 31.

a) lim f(x)
x - -31¯

b) lim f(x)
x - -31

c) lim f(x)
x - (-31)

d) lim f(x)
x - +∞

Question

The graph of f is given. Use the graph to compute the quantities asked for, if a = 31.

a)    lim  f(x)
  x -> -31¯

b)    lim f(x)
  x -> -31

c)    lim f(x)
  x -> (-31)

d)   lim f(x)
  x -> +∞

riley · Answer

Posting a picture of the graph, two secs.  

This limit stuff is owning my brain. =/

riley · Answer

attachment

anonymous · Answer

The graph seems to be the confusing part there! But a limit is essentially what y-value the graph approaches when it gets close to a certain x-value. If a value has a -, it is approached from the left. A value with a + is approached from the right. Is this review so far?

riley · Answer

Yes, all of what you said I understand for the most part.  But I just can't figure out the limits for this graph . . . and I'm not sure where I'm messing up at.  >_<

anonymous · Answer

So let's look at problem (a). It wants you to approach the graph from the left, and find the value of "y" at -a. You'll only look at the part of the graph in Quadrant II, the top left quadrant, because you're coming from the left. At -a (a.k.a -31), the y-value is approaching 2a, so:

$$ \lim_{x \rightarrow -31^{-}}=2a$$

riley · Answer

So the limit would have to be 62, right?

anonymous · Answer

Yes!

riley · Answer

Ahhh okay, I think I was confusing myself with both of the different graphs on 31. . . . I was looking at the closed circle line.

anonymous · Answer

Ah, yes, the +/- will tell you which to look at!

riley · Answer

Ummm, I know that a limit does not exist if the left and right limits do not match up.  So limit as x approaches -31 doesn't exist.  But umm what about f(-31) . . . what is it wanting me to do with that?

riley · Answer

I thought if I was looking at x as it approaches +infinity, then my limit would be positive infinity? since the line doesn't stop . . . but that's not correct Q_Q

anonymous · Answer

As far as the (-31) goes, it should be the same as -31.

For the infinity question: Technically, your answer is right. However, proper notation says that a number approaching infinity doesn't have a limit, therefore the limit does not exist (d.n.e.).

riley · Answer

Oh wow, I guess I was overlooking that rule, that makes sense then.  Okay I think I got this limit graph thing now lol hopefully, thank you again for the help, very very much.

anonymous · Answer

You're very welcome! I'm just now learning limits in Calc, so helping you helps me! :] Good luck!

riley · Answer

Same to you too! =)