What is the limit as n approaches infinity of 2/(sqrt(n))+3/(\sqrt[3]{n)} ?

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limit as n approaches infinity of 2/(sqrt(n))+3/(\sqrt[3]{n)}

n \to \infty lim (\frac{2}{n} + \frac{3}{3 n})

0

Solution steps

n \to \infty lim (\frac{2}{n} + \frac{3}{3 n})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= n \to \infty lim (\frac{2}{n}) + n \to \infty lim (\frac{3}{3 n})

n \to \infty lim (\frac{2}{n}) = 0

n \to \infty lim (\frac{3}{3 n}) = 0

= 0 + 0

Simplify

= 0

x \to 1 - lim (\frac{ln ( x )}{x - 1})

x \to 0 + lim (\frac{cos ^{2} ( x )}{x})

x \to - 2 lim ({- 4})

x \to \frac{1}{3} lim ((2 x) (3 x - 3))

x \to - 1 lim (x^{2} + 2 x)

What is the limit as n approaches infinity of 2/(sqrt(n))+3/(\sqrt[3]{n)} ?
The limit as n approaches infinity of 2/(sqrt(n))+3/(\sqrt[3]{n)} is 0