limit (10) 25 july

**Admin** Mon Jul 25, 2011 9:09 am

limit (10) 25 july

Post Admin Mon Jul 25, 2011 9:09 am

$limit (10) 25 july Gif$

**Admin** Mon Jul 25, 2011 9:30 am

Re: limit (10) 25 july

Post Admin Mon Jul 25, 2011 9:30 am

$limit (10) 25 july Gif.latex?\hspace{-16}\mathbf{\lim_{x\rightarrow%200}\frac{\ln\left(\ln(1-x^2)\right)}{\ln\left(\ln(\cos%20x)\right)}}$\\\\\\%20Now%20at%20$\mathbf{x=0},$%20The%20expression%20is%20$\mathbf{\frac{0}{0}}$%20form.\\\\\\%20So%20We%20can%20use%20$\textbf{D.L.Hospital}$%20Rule.\\\\\\%20$\mathbf{\lim_{x\rightarrow%200}\frac{\frac{1}{\ln(1-x^2)}.\frac{1}{(1-x^2)}.-2x}{\frac{1}{\ln(\cos%20x)}.\frac{1}{\cos%20x}.-\sin%20x}}$\\\\\\%20$\mathbf{\lim_{x\rightarrow%200}\frac{\ln(\cos%20x)}{\ln(1-x^2)}.\frac{\cos%20x}{1-x^2}.\frac{2x}{\sin%20x}}$\\\\\\%20Now%20$\mathbf{\ln(1-x)=-x-\frac{x^2}{2}-\frac{x^3}{3}...........}$\\\\\\%20Now%20at%20$\mathbf{x\rightarrow%200},\;\;$%20Then%20$\mathbf{\ln(1-x)\approx%20-x}$\\\\\\%20So%20$\mathbf{\ln(1-x^2)\approx%20-x^2}$\\\\\\%20similarly%20$\mathbf{\cos%20x=1-\frac{x^2}{2!}+\frac{x^4}{4!}+...........$

$limit (10) 25 july Gif.latex?\hspace{-16}$%20So%20$\mathbf{\lim_{x\rightarrow%200}\frac{\ln(\cos%20x)}{\ln(1-x^2)}.\frac{\cos%20x}{1-x^2}.\frac{-2x}{-\sin%20x}}$\\\\\\%20$\mathbf{\lim_{x\rightarrow%200}\frac{-\frac{x^2}{2!}}{-x^2}.\frac{\cos%20x}{1-x^2}.2$