Question

`lim_(x rightarrow 0) (1 - cos x)/x^2` is equal to ______.

Options

• π

• `1/4`

• `1/2`

• 1

Answer 1

`lim_(x rightarrow 0) (1 - cos x)/x^2` is equal to `underlinebb(1/2)`.

Explanation:

Given, `lim_(x rightarrow 0) (1 - cos x)/x^2`

Applying L' Hospital's rule,

`\implies lim_(x rightarrow 0) (d/dx (1 - cos x))/(d/dx x^2)`

= `lim_(x rightarrow 0)  sinx/(2x)`

Again applying L' Hospital's rule ,

`\implies lim_(x rightarrow 0) (d/dx sinx)/(d/dx 2x) = lim_(x rightarrow 0) cosx/2` 

= `cos0/2`

= `1/2`