Question

If $cosx=b$, then for what b do the roots of the equation form an AP ?

• A. $-1$
• B. $\frac{1}{2}$
• C. $\frac{\sqrt{3}}{2}$
• D. None of these

Answer 1

The correct option is A $-1$

${lim}_{x\to 0}\frac{log(1+x^3)}{si{n}^{3}x}={lim}_{x\to 0}\frac{log(1+x^3)}{x^3}\frac{x^3}{si{n}^{3}x}$

$={lim}_{x\to 0}\frac{d}{dx}\frac{log(1+x^3)}{\frac{d}{dx}}\times 1$

$={lim}_{x\to 0}\frac{\frac{1}{1+x^3}(3x{)}^2}{3x^2}\times 1$

$=1\times 1=1$