limx→0 4x−13sin⁡x4loge⁡1+x23=

# $\underset{x\to 0}{lim} \frac{{\left({4}^{x}-1\right)}^{3}}{\mathrm{sin}\left(\frac{x}{4}\right){\mathrm{log}}_{e}\left(1+\frac{{x}^{2}}{3}\right)}=$

1. A

${\left({\mathrm{log}}_{e}4\right)}^{3}$

2. B

${\mathrm{log}}_{e}4$

3. C

$12{\left({\mathrm{log}}_{e}4\right)}^{3}$

4. D

$5{\left({\mathrm{log}}_{e}4\right)}^{3}$

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### Solution:

$=\underset{x\to 0}{lim} \frac{{\left({4}^{x}-1\right)}^{3}}{\mathrm{sin}\left(\frac{x}{4}\right){\mathrm{log}}_{e}\left(1+\frac{{x}^{2}}{3}\right)}$

Divide with x3 and simplify

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