calculate limits

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calculate limits

Post mohit Tue Jul 19, 2011 1:10 pm

Calculate
$calculate limits Gif$

mohit: Guest

Re: calculate limits

Post Admin Wed Jul 20, 2011 4:00 am

$calculate limits Gif$

Admin: Admin; Posts : 103
Join date : 2011-02-01
Location : India

Re: calculate limits

Post Admin Wed Jul 20, 2011 10:14 am

$calculate limits Gif.latex?\hspace{-17}$\textbf{Here%20We%20have%20to%20find%20Limit%20$\mathbf{\lim_{x\rightarrow%20-1}\frac{\sqrt{\pi}-\sqrt{\cos^{-1}%20x}}{\sqrt{x+1}}}$%20}$\\\\%20\mathbf{x+1\geq%200\Leftrightarrow%20x\geq%20-1}$\\\\%20\textbf{So%20Here%20We%20calculate%20$\mathbf{\lim_{x\rightarrow%20-1\;_{-}}\frac{\sqrt{\pi}-\sqrt{\cos^{-1}%20x}}{\sqrt{x+1}}}$}\\\\%20\textbf{Now%20Let%20$\mathbf{\cos^{-1}x=t\Leftrightarrow%20x=\cos%20t}$}$\\\\%20$\textbf{When%20$\mathbf{x\rightarrow%20-1_{-}\Leftrightarrow%20t\rightarrow%20\pi_{-}}$%20bcz%20$\mathbf{\cos^{-1}x}$%20is%20an%20Decreasing%20function.}$\\\\%20$\textbf{So%20$\mathbf{\lim_{t\rightarrow%20\pi_{-}}\frac{\sqrt{\pi}-\sqrt{t}}{\sqrt{\cos%20t+1}}=\lim_{t\rightarrow%20\pi_{-}}\frac{\left(\pi-t\right)}{\sqrt{\pi}+\sqrt{t}}.\frac{1}{\sqrt{2}.|\cos%20\frac{t}{2}|}}$}\\\\%20\textbf{Now%20Let%20$\mathbf{\frac{\pi}{2}-\frac{t}{2}=u}\Leftrightarrow%20u\rightarrow%200_{+}$}\\\\%20$\mathbf{\lim_{u\rightarrow%200_{+}}\frac{2u}{\left(\sqrt{\pi}+\sqrt{\pi-2u}\right)}\frac{1}{\sqrt{2}}$

Admin: Admin; Posts : 103
Join date : 2011-02-01
Location : India

Re: calculate limits

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