FIND THE LIMIT 2

Calculus Level 2


The answer is 0.

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Aditya Raj by Aditya Raj , 22, India

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2 solutions

Daniel Ferreira
Jun 27, 2015

lim ⁡ x → ∞ ln ⁡ x 2 ( 1 + 2 x 2 ) x 2 ( 1 − 5 x 2 ) = lim ⁡ x → ∞ ln ⁡ 1 + 2 x 2 1 − 5 x 2 = ln ⁡ 1 − 0 1 − 0 = ln ⁡ 1 = 0 \lim_{x \to \infty} \ln \frac{x^2(1 + \frac{2}{x^2})}{x^2(1 - \frac{5}{x^2})} = \\\\ \lim_{x \to \infty} \ln \frac{1 + \frac{2}{x^2}}{1 - \frac{5}{x^2}} = \\\\ \ln \frac{1 - 0}{1 - 0} = \\\\ \ln 1 = \\\\ \boxed{0}

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Please can you explain what happened between the 2nd and 3rd steps?

Ahmed Ali - 5 years, 10 months ago

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O número 2 dividido por infinito tende a zero, assim como o 5.

Daniel Ferreira - 5 years, 10 months ago

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Thank you for trying but I dont understand this language.

Ahmed Ali - 5 years, 9 months ago

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@Ahmed Ali – The number divided by two infinite toward zero, as well as 5.

Daniel Ferreira - 5 years, 9 months ago
Aditya Raj
Apr 20, 2015

Divie nem & deno by x" then we find out ln1 that means zero

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