LIMIT PROBLEM

[HanTxZ]

Help me solve this problem without the use of the de l'Hôpital rule.

lim(x->2) ((2^(x-1)-2)/(x^2+4x-12))

Thanks

 

[Dr.Peterson]

Help me solve this problem without the use of the de l'Hôpital rule.

lim(x->2) ((2^(x-1)-2)/(x^2+4x-12))

Thanks


View attachment 23665

What ARE you allowed to use? Do you know any special limits involving the exponential, for example? Or can you use series?

 

[Romsek]

First thing I'd do is use partial fractions to break the expression into two terms. One of these terms has a trivial limit at [MATH]x=2[/MATH]The remaining term is now linear in the denominator and should be easier to treat.

 

[Deleted member 4993]

WA suggests use of Taylor series (of Taylor Swift fame )....

 

[Steven G]

That is one doozy of an integral.