Question

Find the limit. Use l'Hospital's Rule if appropriate lim x->0 (x(6^x))/((6^x)-1)

Answer 1

not that easy to read

Answer 2

\[\frac{6x^x}{6^x-1}\]?

Answer 3

the bottom is right the top is x6^x

Answer 4

\[\huge \lim_{x\to 0}\frac{x6^x}{6^x-1}\]

Answer 5

yeah thats it

Answer 6

ok it is in the for \(\frac{0}{0}\) take the derivative top and bottom separately

Answer 7

*form

Answer 8

you know the derivative of these?

Answer 9

give me one second to figure them out

Answer 10

here is a huge hint if you need it
for the derivative of the numerator you need the product rule
also \[\frac{d}{dx}b^x=b^x\ln(b)\]

Answer 11

ln(6)x6^x+6^x/ln(6)6^x is that right?

Answer 12

looks right

Answer 13

now replace \(x\) by \(0\) and you are done

Answer 14

i get
\[\frac{1}{\ln(6)}\] but i didn't do it with paper, just looked
see if that is right

Answer 15

thats what i got thanks for the help

Answer 16

yw