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Algebra> Lim[x+x+x.....plese see in image x_#

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Lim[x+x+x.....plese see in imagex_#

ashu , 10 Years ago

Grade 11

1 Answers

Arun Kumar

Last Activity: 10 Years ago

Hi

$\\lim_{x \to \infty}(\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}) \\=>lim_{x \to \infty}(\sqrt{x+\sqrt{x}(1+1/\sqrt{x})^{1/2}}-\sqrt{x}) \\=>lim_{x \to \infty}(\sqrt{x+\sqrt{x}(1+1/2\sqrt{x})}-\sqrt{x}) \\=>lim_{x \to \infty}(\sqrt{x+\sqrt{x}+1/2}-\sqrt{x}) \\=>lim_{x \to \infty}((\sqrt{x}(1+1/\sqrt{x}+1/2x)^{1/2}-\sqrt{x}) \\=>lim_{x \to \infty}((\sqrt{x}(1+1/2\sqrt{x}-\sqrt{x}) \\=1/2$

Please try to understand the intermediate step of binomial approximation.

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

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