A really quick question...

[nbg273]

Can someone give me an example of a limit equation with the definition:

lim f(x) = +/- infinity
x-->a

This is the only type of limit that I can't find an equation for and I've found the other 13 types... It's driving me crazy...

Thanks!

 

[MarkFL]

Can you think of a function with a vertical asymptote at \(\displaystyle x=a\), such that:

\(\displaystyle \displaystyle \lim_{x\to a^{-}}=\pm\infty\)

and:

\(\displaystyle \displaystyle \lim_{x\to a^{+}}=\mp\infty\) ?

 

[nbg273]

Can you think of a function with a vertical asymptote at \(\displaystyle x=a\), such that:

\(\displaystyle \displaystyle \lim_{x\to a^{-}}=\pm\infty\)

and:

\(\displaystyle \displaystyle \lim_{x\to a^{+}}=\mp\infty\) ?

f(x) = (1/x)?

I already have equation examples for:

lim f(x) = +/- infinity
x-->a-
and
x-->a+

but my teacher gave me the definition of just x-->a as well with no "from the right/left."

 

[MarkFL]

f(x) = (1/x)?

Yes, good! For that function we have:

\(\displaystyle \displaystyle \lim_{x\to0^{-}}f(x)=-\infty\)

and

\(\displaystyle \displaystyle \lim_{x\to0^{+}}f(x)=+\infty\)

 

[MarkFL]

...I already have equation examples for:

lim f(x) = +/- infinity
x-->a-
and
x-->a+

but my teacher gave me the definition of just x-->a as well with no "from the right/left."

Can a function approach more than one value at the same value for \(\displaystyle x\) except from different directions?

 

[nbg273]

Can a function approach more than one value at the same value for \(\displaystyle x\) except from different directions?

Yes, so this works! Thanks!