Question

`lim_("x" -> "x" //4) ("cos x - sin x")/("x"- "x" /4)`  is equal to ____________.

Options

• -1

• `2/sqrt2`

• `-2/sqrt2`

• `-1/sqrt2`

Answer 1

`lim_("x" -> "x" //4) ("cos x - sin x")/("x"- "x" /4)`  is equal to `underline(-2/sqrt2)`.

Explanation:

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

`=  lim_("x" -> "x" /4) (-"sin x - cos x")/1`

`= - "sin" pi/4 - "cos" pi/4`

`= -2/sqrt2 = - sqrt2`