Question

If f" = C, C ≠ 0, where C is a constant, then the value of `lim_(x -> 0) (f(x) - 2f (2x) + 3f (3x))/x^2` is

Options

• 0

• 2C

• 20C

• 10C

Answer 1

10C

Explanation:

Given `f^″(x) = C, C ≠ 0` and C is a constant then `lim_(x -> 0) (f(x) - 2f (2x) + 3f (3x))/x^2`

Using L.H. Rule

= `lim_(x -> 0) (f^'(x) - 2f^'(2x).2 + 3f^'(3x).3)/(2x)`

= `lim_(x -> 0) (f^('')(x) - 8f^('')(2x) + 27f^('')(3x))/2`

= `(C - 8C + 27C)/2 = 10C`.