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