Question

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

Options

• 0

• `1/2`

• 1

• `3/2`

Answer 1

`lim_(x rightarrow 0) (e^(x^2) - cosx)/x^2` is equal to `underlinebb(3/2)`.

Explanation:

`lim_(x rightarrow 0) (e^(x^2) - cosx)/x^2`  

= `lim_(x rightarrow 0) (2xe^(x^2) + sinx)/(2x)`  ...`[0/0"form"]` [using L' Hospital Rule]

= `lim_(x rightarrow 0) (2e^(x^2) + 4x^2e^(x^2) + cosx)/2`  ...`[0/0"form"]` [using L' Hospital Rule]

= `(2 + 0 + 1)/2`

= `3/2`