What is the limit as x approaches infinity of \sqrt[x]{2+5^x} ?

The limit as x approaches infinity of \sqrt[x]{2+5^x} is 5

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limit as x approaches infinity of \sqrt[x]{2+5^x}

5

Solution steps

Apply exponent rules

= x \to \infty lim (e^{\frac{1}{x} l n (2 + 5^{x})})

Apply the Limit Chain Rule:

5

= 5

\int_{1}^{5} x^{2} - 6 x + 8 d x

\int 7 x^{4} - 5 x^{3} + 5 x^{2} + C d x

\frac{7}{x}, x = 1, x = 41

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

\frac{d y}{d x} = 2 + 2 y + x + x y

What is the limit as x approaches infinity of \sqrt[x]{2+5^x} ?
The limit as x approaches infinity of \sqrt[x]{2+5^x} is 5