What is the limit as x approaches infinity of b*e^{-x} ?

The limit as x approaches infinity of b*e^{-x} is 0

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limit as x approaches infinity of b*e^{-x}

x \to \infty lim (b \cdot e^{- x})

0

Solution steps

x \to \infty lim (b e^{- x})

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

= b \cdot x \to \infty lim (e^{- x})

Simplify

e^{- x} : \frac{1}{e ^{x}}

= b \cdot x \to \infty lim (\frac{1}{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

= b \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( e ^{x} )}

x \to \infty lim (1) = 1

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

= b \frac{1}{\infty}

Simplify

b \frac{1}{\infty} : 0

= 0

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

x \to \infty lim (6 ln (x))

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

x \to 1 lim ([x^{2} (x + 2)])

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

What is the limit as x approaches infinity of b*e^{-x} ?
The limit as x approaches infinity of b*e^{-x} is 0