What is the limit as n approaches infinity of (3n^{0.4+1}+7n)/(3n^{0.4)+7n} ?

The limit as n approaches infinity of (3n^{0.4+1}+7n)/(3n^{0.4)+7n} is infinity

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limit as n approaches infinity of (3n^{0.4+1}+7n)/(3n^{0.4)+7n}

n \to \infty lim (\frac{3 n ^{0.4 + 1} + 7 n}{3 n ^{0.4} + 7 n})

\infty

Solution steps

n \to \infty lim (\frac{3 n ^{0.4 + 1} + 7 n}{3 n ^{0.4} + 7 n})

Divide by highest denominator power:

\frac{3 n ^{0.4} + 7}{\frac{3}{n ^{0.6}} + 7}

= n \to \infty lim (\frac{3 n ^{0.4} + 7}{\frac{3}{n ^{0.6}} + 7})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{n \to \infty} ( 3 n ^{0.4} + 7 )}{lim _{n \to \infty} ( \frac{3}{n ^{0.6}} + 7 )}

n \to \infty lim (3 n^{0.4} + 7) = \infty

n \to \infty lim (\frac{3}{n ^{0.6}} + 7) = 7

= \frac{\infty}{7}

Apply Infinity Property:

\frac{\infty}{c} = \infty

= \infty

y^{^{''}} + 5 y^{^{'}} = e^{- t}, y (0) = - 0, y^{^{'}} (0) = 1

\int \frac{- y}{cot ( x )} d x

y^{^{''}} + 2 y^{^{'}} - 24 y = 0

x y + y^{^{'}} = 76 x

\int sin (9 x) d x

What is the limit as n approaches infinity of (3n^{0.4+1}+7n)/(3n^{0.4)+7n} ?
The limit as n approaches infinity of (3n^{0.4+1}+7n)/(3n^{0.4)+7n} is infinity