Question

If f′ is continuous, f(7)=0, and f′(7)=11, evaluate

Answer 1

?

Answer 2

\[\lim_{x \rightarrow 0} \frac{ f(7+3x)+f(7+5x)}{ x}\]

Answer 3

@dan815

Answer 4

ok

Answer 5

lhos[itsl since inderminate form

Answer 6

l'hopital*

Answer 7

\[
\lim_{x \rightarrow 0} \frac{ f(7+3x)+f(7+5x)}{ x} = \lim_{x \rightarrow 0} \frac{ f(7+3x)}{x} +\lim_{x \rightarrow 0} \frac{(7+5x)}{ x} = \\
\lim_{x \rightarrow 0} 3\frac{ f(7+3x)}{3x} +\lim_{x \rightarrow 0} 7\frac{(7+5x)}{ 7x}
\]

Answer 8

= 3f'(7) + 7f'(7)