Finding the limit using a graph

[ScienceJen]

Hi everyone,

Thanks for all of your help. I hope I'm not posting too much.

I understand a)-c), but not d). If x is approaching negative 4 from the right, would the limit of f(x) - the y-axis - be infinity, not negative infinity? Isn't it the x-axis that is going to - infinity on the left-side of the graph?

 

[Dr.Peterson]

Hi everyone,

Thanks for all of your help. I hope I'm not posting too much.

I understand a)-c), but not d). If x is approaching negative 4 from the right, would the limit of f(x) - the y-axis - be infinity, not negative infinity? Isn't it the x-axis that is going to - infinity on the left-side of the graph?

View attachment 31825

I'm not quite sure what you're thinking, but here is what the limit (d) means:



As x approaches -4 from the right, the y-coordinate on the graph moves down, toward negative infinity. So we're following the curve moving to the left, and thinking about what is happening to y.

So the limit is [imath]-\infty[/imath].

 

[lev888]

d is the same idea as a. You wrote that you understood a.

 

[Shiloh]

Perhaps you are just using the wrong words but the x and y axes have nothing to do with (d).
As x approaches -4 from the right, the (x, y) point moves down the graph, away from both axes, without bound. The limit is "negative infinity". \(\displaystyle \lim_{x\to -4^+}= -\infty\).

 

[ScienceJen]

I'm not quite sure what you're thinking, but here is what the limit (d) means:

View attachment 31826

As x approaches -4 from the right, the y-coordinate on the graph moves down, toward negative infinity. So we're following the curve moving to the left, and thinking about what is happening to y.

So the limit is [imath]-\infty[/imath].

Ok I see what you are saying. I was looking at how x approaches -4 from the right around (just to the right of) -4, not from zero. So, when I looked at what is happening to y, I saw it going to positive infinity once x hits -4. Guess I should be thinking about this question in terms of as x approaches -4 from zero?
Thank you.

 

[lev888]

I was looking at how x approaches -4 from the right around (just to the right of) -4, not from zero.

From the right IS from zero. 0 to -4 is moving from right to left.

 

[ScienceJen]

From the right IS from zero. 0 to -4 is moving from right to left.

Awesome! Thanks for clearing that up, lev888. All of you are so much help and I appreciate it so much.