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limits problem1

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limits problem1 Empty limits problem1

Post  mohit Wed Jul 20, 2011 11:30 am

limits problem1 Gif

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limits problem1 Empty another question

Post  mohit Wed Jul 20, 2011 11:40 am

limits problem1 Gif.latex?$Find%20value%20of%20$\mathbf{a}$%20and%20$\mathbf{b}$%20in%20$\mathbf{\lim_{x\rightarrow%200}\frac{x

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limits problem1 Empty problem2,.......

Post  mohit Wed Jul 20, 2011 11:51 am

limits problem1 Gif

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limits problem1 Empty Re: limits problem1

Post  Admin Wed Jul 20, 2011 12:33 pm

limits problem1 Gif
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limits problem1 Empty Re: limits problem1

Post  Admin Thu Jul 21, 2011 7:17 am

one solution for (1)

limits problem1 Gif.latex?\hspace{-18}$Let%20$\mathbf{y=\sqrt{x^2+\sqrt{x^4+1}}}$\\\\%20$\mathbf{y^2=x^2+\sqrt{x^4+1}}$\\\\%20$\mathbf{\left(y^2-x^2\right)^2=x^4+1}$\\\\%20$\mathbf{y^4+x^4-2x^2.y^2=x^4+1}$\\\\%20$\mathbf{y^2.\left(y^2-2x^2\right)=1}$\\\\%20so%20$\mathbf{y\neq\pm\sqrt{2}.x}$%20and%20$\mathbf{y\neq%200}$\\\\%20so%20Here%20$\mathbf{y=\pm\sqrt{2}.x,\;\;%20y=0}$%20are%20the%20asymptodes.\\\\%20so%20$\mathbf{\lim{x\rightarrow%20\infty}\left(y-\sqrt{2}
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limits problem1 Empty q. remaining

Post  mohit Thu Jul 21, 2011 12:12 pm

whats the meaning of asymtodes......... & sir one question is remaining in which values of a & b are to be found...

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Post  Admin Thu Jul 21, 2011 8:53 pm

limits problem1 Gif.latex?\hspace{-15}\mathbf{\lim_{x\rightarrow%200}\frac{x.(1+a\cos%20x)-b\sin%20x}{x^3}=1}$\\\\\\%20Using%20expansion%20of%20$\mathbf{\sin%20x}$%20and%20$\mathbf{\cos%20x},$%20We%20get%20\\\\\\%20$\mathbf{\lim_{x\rightarrow%200}\frac{x.\left\{1+a.\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}.....\right)-b.\left(x-\frac{x^3}{3!}+\frac{x^5}{5!}....\right)\right\}}{x^3}=1}$\\\\\\%20$\mathbf{\lim_{x\rightarrow%200}\frac{x+ax-\frac{ax^3}{2}-bx-\frac{bx^3}{6}....}{x^3}=1}$\\\\\\%20$\mathbf{\lim_{x\rightarrow%200}\frac{x.(1+a-b)-x^3.\left(\frac{a}{2}+\frac{b}{6}\right)+...
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