Answer:
application of L'Hopital's rule to the presumed indeterminate form yields this conclusion
Step-by-step explanation:
This is a reverse application of L'Hopital's rule for determining the limits involving indeterminate forms.
When the expression evaluated at the limit is 0/0, then L'Hopital's rule tells you the limit can be found from n'/d', where n and d are the numerator and denominator of the original expression, respectively.
We can see that x-π = 0 at x=π, so we assume that f(π) = 0 as well, and the expression n/d = f(x)/(x-π) evaluates to the indeterminate form 0/0.
The derivatives are ...
n' = f'(x)
d' = 1
Then we have the limit as ...
lim{x→π) = n'/d' = f'(π)/1 = 3 ⇒ f'(π) = 3
The conclusion f(π)=0 and f'(π)=3 follows from L'Hopital's Rule.
