Question

Let p = `lim_(x rightarrow 0^+)(1 + tan^2sqrt(x))^(1/(2x))` then log p is equal to ______.

Options

• `1/2`

• `1/4`

• 2

• 1

Answer 1

Let p = `lim_(x rightarrow 0^+)(1 + tan^2sqrt(x))^(1/(2x))` then log p is equal to `underlinebb(1/2)`.

Explanation:

In p = `lim_(x rightarrow 0^+) 1/(2x)` In`(1 + tan^2sqrt(x))`

`lim_(x rightarrow 0^+) 1/x` In`(sec sqrt(x))`

Applying L hospital's rule :

= `lim_(x rightarrow 0^+) (secsqrt(x) tansqrt(x))/(secsqrt(x).2sqrt(x))`

= `lim_(x rightarrow 0^+) (tansqrt(x))/(2sqrt(x))` 

= `1/2`