Question

If f′ is continuous, f(8)=0, and f′(8)=14, evaluate
`\lim_(x \to \zero0) (f(8+3x)(8+5x))/(x)`

Answer 1

-30

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!!