Knownothing Knownothing

16-03-2019
Mathematics

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If f′ is continuous, f(8)=0, and f′(8)=14, evaluate [tex]\lim_{x \to \zero0} \frac{f(8+3x)(8+5x)}{x}[/tex]

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Аноним Аноним

16-03-2019

Answer:

-30

Step-by-step explanation:

lim(x→0) (f(8+3x) - f(8+5x))/x; this is a limit of the form 0/0

= lim(x→0) (3 f'(8+3x) - 5 f'(8+5x))/1, by L'Hopital's Rule (and Chain Rule)

= 3 f'(8) - 5 f'(8)

= -2 f'(8)

= -2 * 15

= -30

hope i helped!!

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