Question

Find the limit if it exists.

Answer 1

\[\lim_{h \rightarrow 0} [(a+h)^4 - a^4] / h\]

Answer 2

so we know that if we have a polynomial that the limit of the function is the polynomial evaluated at that point in question. if we have a quotient we have the limit of the top over the limit of the bottom. however, here we have h=0 in the bottom so does that mean that the limit does not exist? Maybe it's an obvious question

Answer 3

i guess what my question is simply b/c we have lim(numerator)/limit(denominator)
if the limit(denominator) is equal to 0 is that sufficient to say that the limit does not exist?

Answer 4

the limit of both the denominator and the numerator are going to zero so you have to use hospitals rule if you know it?

Answer 5

well actually i'm trying to help a buddy and i'm not sure if they are that far yet. if they aren't would anything else work?

Answer 6

i'll go with that thank you :-)

Answer 7

welcome :D