Question

The value of `lim_(x rightarrow 0) (4^x - 1)^3/(sin  x^2/4 log(1 + 3x))`, is ______.

विकल्प

• `4/3("In"  4)^2`

• `4/3("In"  4)^3`

• `3/2("In"  4)^2`

• `3/2("In"  4)^3`

Answer 1

The value of `lim_(x rightarrow 0) (4^x - 1)^3/(sin  x^2/4 log(1 + 3x))`, is `underlinebb(4/3("In"  4)^3)`.

Explanation:

`lim_(x rightarrow 0) (4^x - 1)^3/(sin  x^2/4 log(1 + 3x))`

= `lim_(x rightarrow) (4^x - 1)^3/x^3.(x//2)^2/(sin  x^2//4). (3x)/(log(1 + 3x)). 4/3`

= `4/3(log_e 4)^3. 1.log_e(e)`

= `4/3(log_e 4)^3`.