What is the limit as x approaches infinity of (e^{2/x}sin(pix))/(x+2)+x ?

The limit as x approaches infinity of (e^{2/x}sin(pix))/(x+2)+x is Does not exist

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limit as x approaches infinity of (e^{2/x}sin(pix))/(x+2)+x

x \to \infty lim (\frac{e ^{\frac{2}{x}} sin ( π x )}{x + 2} + x)

Does not exist

Solution steps

x \to \infty lim (\frac{e ^{\frac{2}{x}} sin ( π x )}{x + 2} + x)

Factor out

\frac{e ^{\frac{2}{x}} sin ( π x )}{x + 2}

from

\frac{e ^{\frac{2}{x}} sin ( π x )}{x + 2} + x : \frac{e ^{\frac{2}{x}} sin ( π x )}{x + 2} 1 + \frac{x}{\frac{e ^{\frac{2}{x}} s i n ( π x )}{x + 2}}

= x \to \infty lim \frac{e ^{\frac{2}{x}} sin ( π x )}{x + 2} 1 + \frac{x}{\frac{e ^{\frac{2}{x}} s i n ( π x )}{x + 2}}

\frac{e ^{\frac{2}{x}} sin ( π x )}{x + 2} 1 + \frac{x}{\frac{e ^{\frac{2}{x}} s i n ( π x )}{x + 2}}

undefined for

x

approaching

\infty

= Does not exist

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What is the limit as x approaches infinity of (e^{2/x}sin(pix))/(x+2)+x ?
The limit as x approaches infinity of (e^{2/x}sin(pix))/(x+2)+x is Does not exist