Question

Solve $\underset{x\to 0}{Lt}\frac{x{2}^{3x}-x}{1-\cos \left(3x\right)}$

• A. $\frac{2}{9}\log 2$
• B. $\frac{2}{3}\log 4$
• C. $\frac{4}{3}\log 2$
• D. $\frac{1}{3}\log 2$

Answer 1

Answer: (A)

$\frac{2}{9}\log 2$

${lim}_{x\to 0}\frac{x{2}^{3x}-x}{1-cos\left(3x\right)}=\frac{0}{0}$ form.

by L,Hospital's Rule.

${lim}_{x\to 0}\frac{2^{3x}+x{2}^{3x}log2-1}{3\left(sin3x\right)}=\frac{0}{0}$ From again L' Hospital's Rule.

${lim}_{x\to 0}\frac{2^{3x+1}log2+x{.2}^{3x}(log2{)}^2}{9cos3x}=\frac{2log2}{9}$ Ans