Do I Need to Rationalise?

Calculus Level 4

lim ⁡ n → ∞ n 3 − 2 n 2 + 1 + n 4 + 1 3 n 6 + 6 n 5 + 2 4 − n 7 + 3 n 3 + 1 5 \large \lim_{n\to\infty} \frac{\sqrt[]{n^3 -2n^2 +1}+ \sqrt[3]{n^4 +1}}{\sqrt[4]{n^6+6n^5+2} - \sqrt[5]{n^7+3n^3+1}}

Find the value of the limit above.

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Thomas Jacob by Thomas Jacob , 19, India

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3 solutions

Numerator and denominator have equal degrees, so the answer is the coefficient of the greatest degree in numerator ( 1 1 ) divided into the coefficient of te greatest degree in denominator ( 1 1 ), this is 1 1 = 1 \frac{1}{1}=1

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Could you please verify if you can say that n is a natural number? I'm not sure because you have put n tends to infinity and we do not know what infinity is and we cannot definitely say it is a natural number. Please correct me if I am wrong. Cheers

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Oops! Didn't realize that. I'll change it to just "Find the value of the limit above". Thanks for pointing that out :)

Thomas Jacob - 4 years, 4 months ago

multiply numerator and denominator by n − 3 2 n^{-\tfrac{3}{2}}

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