Evaluate limit, as x -> a, of (e^(x^2) - e^(a^2)) / (x - a)

[jmorris1]

lim as x approaches a of (e[sup:3gadh2lh]x^2[/sup:3gadh2lh] - e[sup:3gadh2lh]a^2[/sup:3gadh2lh])/(x - a)

Don't know where to start with this one. Any help would be greatly appreciated. I thought about the various was to work limits, i.e. factoring, etc. Couldn't seem to come up with the right one.

 

[Deleted member 4993]

Re: Evaluate a limit

lim as x approaches a of (e[sup:jou4hdf3]x^2[/sup:jou4hdf3] - e[sup:jou4hdf3]a^2[/sup:jou4hdf3])/(x - a)

Don't know where to start with this one. Any help would be greatly appreciated. I thought about the various was to work limits, i.e. factoring, etc. Couldn't seem to come up with the right one.

Replace x = a + h

then take the limit to h -> 0

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[PAULK]

lim as x approaches a of (e[sup:25wmqx7t]x^2[/sup:25wmqx7t] - e[sup:25wmqx7t]a^2[/sup:25wmqx7t])/(x - a)

Don't know where to start with this one. Any help would be greatly appreciated. I thought about the various was to work limits, i.e. factoring, etc. Couldn't seem to come up with the right one.

You start by remembering. If you have to dunk yourself in a tank of water three times to remember, then do that: (from an old Sid Caesar sketch)

Remember one form of the definition of the derivative at x = a:

f'(a) =

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

Now put that together with your example:

lim (ex^2 - ea^2)/(x - a)
x->a

Remind you of anything?