Help with Limits

[zzinfinity]

I'm having trouble with 2 limits problems. If you can help with either, that would be great.

1. Lim ((3[sup:1j67559c]2[/sup:1j67559c]-1)/x) as x approaches 0

For this one I don't really even know where to start. Conjugates maybe? but I'm not quite sure how to use those in this situation

and

2. Lim (e[sup:1j67559c]t[/sup:1j67559c]/t) - (1/t) as t approaches 0 from the right hand side

For this one I combined the fractions to get (e[sup:1j67559c]t[/sup:1j67559c]-1)/t) but then was unsure what to do from there. I tried taking the natural log of the numerator and the denominator, but I did not know what to do after that. Any thoughts?

Thanks for your help!

 

[mmm4444bot]

(3[sup:34dh59k5]2[/sup:34dh59k5]-1)/x

Please check this expression for typographical error(s).

 

[lookagain]

I'm having trouble with 2 limits problems. If you can help with either, that would be great.

1. Lim ((3[sup:3unt8n26]x[/sup:3unt8n26]-1)/x) as x approaches 0

There is a typo. It must be the above change in the quote box.

You may use L'Hospital's rule:

Lim (3[sup:3unt8n26]x[/sup:3unt8n26](ln(3))/1 (as x approaches 0) = ln(3)

 

[lookagain]

Lim (e[sup:26xp38yh]t[/sup:26xp38yh]/t) - (1/t) as t approaches 0 from the right hand side

2.

Rewrite it as:

Lim ((e[sup:26xp38yh]t[/sup:26xp38yh] - 1)/t) (as t approaches 0[sup:26xp38yh]+[/sup:26xp38yh])

If you use L'Hospital's rule:

Lim (e[sup:26xp38yh]t[/sup:26xp38yh]/1) (as t aproaches 0[sup:26xp38yh]+[/sup:26xp38yh]) = e[sup:26xp38yh]0[/sup:26xp38yh] = 1