Simple Limits!

Calculus Level 1

Find the limit.


The answer is 1.

Abhi Kumbale by Abhi Kumbale , 21, India

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2 solutions

Abhi Kumbale
Feb 27, 2015

Rewrite like this and evaluate.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Or use L'Hôpital's rule.

Prasun Biswas - 6 years, 3 months ago
Daniel Ferreira
Aug 1, 2015

lim ⁡ n → ∞ 3 n 3 n − 1 = lim ⁡ n → ∞ 3 n 3 n ( 1 − 1 3 n ) = lim ⁡ n → ∞ 1 1 − 1 3 n = 1 1 − 0 = 1 \\ \lim_{n \to \infty} \frac{3^n}{3^n - 1} = \\\\\\ \lim_{n \to \infty} \frac{3^n}{3^n\left ( 1 - \frac{1}{3^n} \right )} = \\\\\\ \lim_{n \to \infty} \frac{1}{1 - \frac{1}{3^n}} = \\\\\\ \frac{1}{1 - 0} = \\\\ \boxed{\boxed{1}}

0 Helpful 0 Interesting 0 Brilliant 1 Confused

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