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

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

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

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

0

Solution steps

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

Simplify

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

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

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

b \to \infty lim (1) = 1

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

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

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

x \to - \infty lim (7^{x})

x \to π lim (\frac{cos ( 2 x )}{x})

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

h \to 5 lim (5 - h)

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