What is the limit as x approaches infinity of 5^x-1 ?

The limit as x approaches infinity of 5^x-1 is infinity

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limit as x approaches infinity of 5^x-1

x \to \infty lim (5^{x} - 1)

\infty

Solution steps

x \to \infty lim (5^{x} - 1)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim (5^{x}) - x \to \infty lim (1)

x \to \infty lim (5^{x}) = \infty

x \to \infty lim (1) = 1

= \infty - 1

Apply Infinity Property:

\infty - c = \infty

= \infty

x \to 6 lim (\frac{x - 3}{x + 8})

x \to 0 lim (x^{t a n (x^{2})})

x \to 0 lim (\frac{1}{x} - \frac{1}{2 x ^{2}})

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

x \to - \infty lim (ln (1))

What is the limit as x approaches infinity of 5^x-1 ?
The limit as x approaches infinity of 5^x-1 is infinity