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

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

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

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

2

Solution steps

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

Divide by

e^{x} : \frac{2 - \frac{3}{e ^{x}}}{1 + \frac{5}{e ^{x}}}

= x \to \infty lim (\frac{2 - \frac{3}{e ^{x}}}{1 + \frac{5}{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} ( 2 - \frac{3}{e ^{x}} )}{lim _{x \to \infty} ( 1 + \frac{5}{e ^{x}} )}

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

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

= \frac{2}{1}

Simplify

= 2

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

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

x \to 3 lim (x - 4)

x \to - \infty lim (3^{x} - 2)

x \to (2) lim (\frac{x ^{2} + 2 x - 3}{3 x ^{2} + 3 x - 18})

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