Question

lim 5^t - 3^t / t (l'hospital's rule section)
t->0

Answer 1

Is that
\[\lim_{t \rightarrow 0}(5^t-\frac{3^t}{t}) \text{ or } \lim_{t \rightarrow 0}\frac{5^t-3^t}{t}\]

Answer 2

I think you might mean the second one in which case plugin' in 0 will give you 0/0
which means we can use l'hospital's rule

Answer 3

\[\lim_{t \rightarrow 0}\frac{5^t-3^t}{t}=\lim_{t \rightarrow 0}\frac{(5^t-3^t)'}{(t)'}\]

Answer 4

I'm assuming your trouble is with the top?

Answer 5

\[\text{ if } y=a^x \text{ and } a>0 \text{ then } y'=a^x \cdot \ln(a)\]

Answer 6

yes, so i have \[\frac{5^{t}\ln 5 - 3^{t} \ln 3 }{1}\]

Answer 7

ok great now plug in 0

Answer 8

i get ln 5 - ln 3 which is about .51 on calc... but answer given is \[\ln \frac{5}{3}\]

Answer 9

\[\ln(5)-\ln(3)=\ln(\frac{5}{3})\]

Answer 10

by properties of log

Answer 11

oh yeah.

Answer 12

ty

Answer 13

np