Question

`lim_("x" -> 0) (1 - "cos" 4 "x")/"x"^2` is equal to ____________.

विकल्प

• 0

• 8

• None of these

• `1/2`

Answer 1

`lim_("x" -> 0) (1 - "cos" 4 "x")/"x"^2` is equal to 8.

Explanation:

`=  lim_("x" -> 0) (1 - "cos" 4 "x")/"x"^2`

`=  lim_("x" -> 0) (4  "sin"  4 "x")/(2 "x")`

`=  lim_("x"  -> 0) (16  "cos"  4 "x")/2 = 8` (using L’Hospital Rule)