What is the limit as x approaches-infinity of (2^x-1)/(3^x+4) ?

The limit as x approaches-infinity of (2^x-1)/(3^x+4) is -1/4

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limit as x approaches-infinity of (2^x-1)/(3^x+4)

x \to - \infty lim (\frac{2 ^{x} - 1}{3 ^{x} + 4})

- \frac{1}{4}

Decimal

- 0.25

Solution steps

x \to - \infty lim (\frac{2 ^{x} - 1}{3 ^{x} + 4})

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 ^{x} - 1 )}{lim _{x \to - \infty} ( 3 ^{x} + 4 )}

x \to - \infty lim (2^{x} - 1) = - 1

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

= \frac{- 1}{4}

Simplify

= - \frac{1}{4}

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x \to - \frac{5}{2} lim (\frac{( 8 x ^{3} + 125 )}{6 x ^{2} + 23 x + 20})

x \to \infty lim (14 x)

What is the limit as x approaches-infinity of (2^x-1)/(3^x+4) ?
The limit as x approaches-infinity of (2^x-1)/(3^x+4) is -1/4