What is the limit as x approaches infinity of (3e^x-4)/(5e^x+2) ?

The limit as x approaches infinity of (3e^x-4)/(5e^x+2) is 3/5

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limit as x approaches infinity of (3e^x-4)/(5e^x+2)

x \to \infty lim (\frac{3 e ^{x} - 4}{5 e ^{x} + 2})

\frac{3}{5}

Decimal

0.6

Solution steps

x \to \infty lim (\frac{3 e ^{x} - 4}{5 e ^{x} + 2})

Divide by

e^{x} : \frac{3 - \frac{4}{e ^{x}}}{5 + \frac{2}{e ^{x}}}

= x \to \infty lim (\frac{3 - \frac{4}{e ^{x}}}{5 + \frac{2}{e ^{x}}})

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 _{x \to \infty} ( 3 - \frac{4}{e ^{x}} )}{lim _{x \to \infty} ( 5 + \frac{2}{e ^{x}} )}

x \to \infty lim (3 - \frac{4}{e ^{x}}) = 3

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

= \frac{3}{5}

x \to 0 + lim (x arctan (\frac{1}{x}))

x \to 0 lim (5 x + 3)

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

x \to 0 lim (e^{\frac{4}{x}})

x \to 4 + lim (x^{2} - 12)

What is the limit as x approaches infinity of (3e^x-4)/(5e^x+2) ?
The limit as x approaches infinity of (3e^x-4)/(5e^x+2) is 3/5