Question

If f'(1) = 3 and f'(2) = 2, then the value of `lim_(h→0) (f(1 + 2h) - f(1))/(f(2 + 3h) - f(2))` is equal to ______.

Options

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

If f'(1) = 3 and f'(2) = 2, then the value of `lim_(h→0) (f(1 + 2h) - f(1))/(f(2 + 3h) - f(2))` is equal to 1.00.

Explanation:

`lim_(h→0) (f(1 + 2h) - f(1))/(f(2 + 3h) - f(2)) = lim_(h→0) (f^'(1 + 2h).2)/(f^'(2 + 3h).3)`

= `2/3.(f^'(1))/(f^'(2))`

= 1