Question

$\underset{x\to 0}{lim}\frac{1-co{s}^{3}x+si{n}^{3}x+\ell n(1+x^3)+\ell n(1+cosx)}{x^2-1+2co{s}^{2}x+ta{n}^{4}x+si{n}^{3}x}$ is equal to -

• A. $\frac{3}{4}$
• B. $ln2$
• C. $\frac{ln2}{4}$
• D. $3/2$

Answer 1

The correct option is B $ln2$

$\underset{x\to 0}{lim}\frac{1-co{s}^{3}x+si{n}^{3}x+\ell n(1+x^3)+\ell n(1+cosx)}{x^2-1+2co{s}^{2}x+ta{n}^{4}x+si{n}^{3}x}$
$=\frac{1-1+0+\ln (1+0)+\ln (1+1)}{0-1+2+0+0}=\ln 2$