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

The limit as x approaches infinity of e^{-3x}sin(x) is 0

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limit as x approaches infinity of e^{-3x}sin(x)

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

0

Solution steps

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

Simplify

e^{- 3 x} : \frac{1}{e ^{3 x}}

= x \to \infty lim (\frac{1}{e ^{3 x}} sin (x))

Simplify

\frac{1}{e ^{3 x}} sin (x) : \frac{sin ( x )}{e ^{3 x}}

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

Apply the Squeeze Theorem:

0

= 0

What is the limit as x approaches infinity of e^{-3x}sin(x) ?
The limit as x approaches infinity of e^{-3x}sin(x) is 0