What is the limit as x approaches infinity of e^{1/x}sin(1/x) ?

The limit as x approaches infinity of e^{1/x}sin(1/x) is 0

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limit as x approaches infinity of e^{1/x}sin(1/x)

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

0

Solution steps

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

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

x \to \infty lim (sin (\frac{1}{x})) = 0

= 1 \cdot 0

Simplify

= 0

What is the limit as x approaches infinity of e^{1/x}sin(1/x) ?
The limit as x approaches infinity of e^{1/x}sin(1/x) is 0