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Question
The value of `lim_(x rightarrow 0) (4^x - 1)^3/(sin x^2/4 log(1 + 3x))`, is ______.
Options
`4/3("In" 4)^2`
`4/3("In" 4)^3`
`3/2("In" 4)^2`
`3/2("In" 4)^3`
MCQ
Fill in the Blanks
Solution
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`.
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