What is the limit as x approaches infinity of-e^{3x}+100e^{3(x-1)} ?

The limit as x approaches infinity of-e^{3x}+100e^{3(x-1)} is infinity

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limit as x approaches infinity of-e^{3x}+100e^{3(x-1)}

x \to \infty lim (- e^{3 x} + 100 e^{3 (x - 1)})

\infty

Solution steps

x \to \infty lim (- e^{3 x} + 100 e^{3 (x - 1)})

Factor out

e^{3 x}

from

- e^{3 x} + 100 e^{3 (x - 1)} : e^{3 x} (- 1 + \frac{- 100 e ^{3 (x - 1)}}{- e ^{3 x}})

= x \to \infty lim (e^{3 x} (- 1 + \frac{- 100 e ^{3 (x - 1)}}{- e ^{3 x}}))

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

With the exception of indeterminate form

= x \to \infty lim (e^{3 x}) \cdot x \to \infty lim (- 1 + \frac{- 100 e ^{3 (x - 1)}}{- e ^{3 x}})

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

x \to \infty lim (- 1 + \frac{- 100 e ^{3 (x - 1)}}{- e ^{3 x}}) = - 1 + \frac{100}{e ^{3}}

= \infty \cdot (- 1 + \frac{100}{e ^{3}})

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 0 lim (\frac{( 7 ^{x} - 8 ^{x} )}{x})

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

x \to \infty lim (\frac{( 5 ^{x} + x ^{4} )}{( 7 ^{x} + x ^{2} )})

x \to - 3 - lim (\frac{x + 1}{x ^{2} - 9})

x \to π lim (sin^{2} (x))

What is the limit as x approaches infinity of-e^{3x}+100e^{3(x-1)} ?
The limit as x approaches infinity of-e^{3x}+100e^{3(x-1)} is infinity