Limit

[nikchic5]

If f' is continuous, f(9)=0 and f'(9)=8, evaluate the
limit as x approaches 0 for
( f (9 + 7x) + f (9 + 8x) ) / ( x )

Thanks so much for any help!

 

[royhaas]

Are you supposed to use L'Hospital's Rule? If not, start with
f(9+7x)/x = 7( f(9+7x)-f(9))/(7x).

 

[nikchic5]

Ok...

Hey I don't think I need to use L'Hospitals rule....so where do I go from there?

 

[pka]

\(\displaystyle \L
\begin{array}{l}
\frac{{f(9 + 7x) + f(9 + 8x)}}{x} = 7\frac{{f(9 + 7x) - f(9)}}{{7x}} + 8\frac{{f(9 + 8x) - f(9)}}{{8x}} \\
lim_{7x \to 0} 7\frac{{f(9 + 7x) - f(9)}}{{7x}} = 7f'(9) \\
\end{array}\).

Can you finish it?

 

[nikchic5]

Ok...

Yes...I got the answer as 120; Is that correct? Thanks so much