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Limit to infinity

Suppose that f(x) diffirentiabel f'(x)=1/{x^2+f(x)^2} and f(1)=1, find lim x to infinity f(x)

Note by Pebrudal Zanu
4 years, 5 months ago

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Guive Chafai - 4 years, 5 months ago

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0 can't be the answer as the the slope is 1/2 at x = 1 and as x tends to infinity f'(x) remains always positive and tends to zero, hence the function keeps increasing from x = 1 and approaches some maximum value which is less than infinity but greater than 1.

Lokesh Sharma - 4 years, 5 months ago

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Someone..

Pebrudal Zanu - 4 years, 5 months ago

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It can be written as dy/dx=1/(x^2+y^2) I don't know how to solve it but it seems to me a first order non-linear ordinary differential equation.

If you know how to solve this differential equation you can find the function and hence the limit. OR if you just need the answer try WolframAlpha or something like that to solve the differential equation.

Hope this would help!

Lokesh Sharma - 4 years, 5 months ago

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