What is the limit as n approaches infinity of \sqrt[n]{(1+2^n+3^n)} ?

The limit as n approaches infinity of \sqrt[n]{(1+2^n+3^n)} is 3

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limit as n approaches infinity of \sqrt[n]{(1+2^n+3^n)}

n \to \infty lim (n (1 + 2^{n} + 3^{n}))

3

Solution steps

n \to \infty lim (n 1 + 2^{n} + 3^{n})

Apply exponent rules

= n \to \infty lim (e^{\frac{1}{n} l n (1 + 2^{n} + 3^{n})})

Apply the Limit Chain Rule:

3

= 3

h \to 0 lim (\frac{( 3 - 9 + h )}{h})

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

x \to c lim (a x + b)

x \to - \infty lim (\frac{x ^{2} + 4}{x + 7})

x \to 2 lim (\frac{x ^{2} + x - 6}{x ^{3} - 9 x})

What is the limit as n approaches infinity of \sqrt[n]{(1+2^n+3^n)} ?
The limit as n approaches infinity of \sqrt[n]{(1+2^n+3^n)} is 3