A) 4
B) 5
C) 6
D) 8
Correct Answer: C
Solution :
| \[\underset{x\to 0}{\mathop{Lim}}\,\frac{{{3}^{6x}}-{{3}^{5x}}-{{3}^{4x}}+{{3}^{2x}}+{{3}^{x}}-1}{{{x}^{3}}}\] |
| =\[\underset{x\to 0}{\mathop{Lim}}\,\frac{({{3}^{x}}-1)({{3}^{5x}}-{{3}^{3x}}-{{3}^{2x}}+1)}{{{x}^{3}}}\] |
| =\[\underset{x\to 0}{\mathop{Lim}}\,\frac{({{3}^{x}}-1)({{3}^{2x}}-1)({{3}^{3x}}-1)}{{{x}^{3}}}\] |
| =\[(\ell n3)\,\,(2\ell n3)\,\,(3\ell n3)=\,6{{(\ell n3)}^{3}}\] |
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