Thread: Limits with infinity

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(a) lim f(x)
x-> infinity

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

(c) lim f(x)
x->1

(d) lim f(x)
x-> 3

(e) the equations of the asymptotes (Enter your answers as comma-separated lists.)

Vertical?

Horizontal?

For infinity limits would is it the same left and right? Also how do you tell the vertical and horizontal asymptotes?

Err meant with infinity limits is it the same as in negative is left and positive is right.

Positive infinity is "all the way" to the right, negative is "all the way" to the left.

Spots where the line never touches, but always get closer and closer to, are asymptotes. An example of avertical asymptote would be on you graph at x=3. Notice the graph never touches it? Now, imagine the line going to the right, forever. It seems like it would never go past y=-2, that means that we have a horizontal asymptote at y=-2.

What do you mean won't go past y= -2

So, is a) -2 b)2 c)infinity d) - infinity and the asymptotes I have no clue about still.

You got the limits right. I mean the line will never cross an asymptote. If I have a horizontal asymptote at x=2, the x value of the line will either always be higher than two, or lower than two, but it will never equal two. Think about the graph of It would have a vertical asymptote at x=3, because if you plug 3 into the fraction, you would have and that is an undefined fraction. So what points on your graph does the line never touch? Hint, the horizontal asymptotes are also limits.