BITSAT 2009
- Exam
- BITSAT
- Year
- 2009
- Subject
- Mathematics
- Chapter
- Functions
BITSAT 2009 · Mathematics · Functions
The value of ( _ x arrow 0 ((4^x-1)^3)/( (x^2)/(4) (1+3 x))), is
The value of (\lim _{x \rightarrow 0} \frac{\left(4^x-1\right)^3}{\sin \frac{x^2}{4} \log (1+3 x)}), is
Options
- A(\frac{4}{3}(\ln 4)^2)
- B(\frac{4}{3}(\ln 4)^3)
- C(\frac{3}{2}(\ln 4)^2)
- D(\frac{3}{2}(\ln 4)^3)
Correct answer
B. (\frac{4}{3}(\ln 4)^3)
Step-by-step solution
(
x→0limsin4x2log(1+3x)(4x−1)3=x→0limx3(4x−1)3⋅sinx2/4(x/2)2⋅log(1+3x)3x⋅34=34(loge4)3⋅1⋅loge(e)=34(loge4)3.)
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