What is the limit as x approaches 0-of (e^{2/x}*sin(pi(x)))/(x+2)+x ?

The limit as x approaches 0-of (e^{2/x}*sin(pi(x)))/(x+2)+x is 0

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limit as x approaches 0-of (e^{2/x}*sin(pi(x)))/(x+2)+x

x \to 0 - lim (\frac{e ^{\frac{2}{x}} \cdot sin ( π ( x ) )}{x + 2} + x)

0

Solution steps

x \to 0 - lim (\frac{e ^{\frac{2}{x}} sin ( π x )}{x + 2} + x)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 - lim (\frac{e ^{\frac{2}{x}} sin ( π x )}{x + 2}) + x \to 0 - lim (x)

x \to 0 - lim (\frac{e ^{\frac{2}{x}} sin ( π x )}{x + 2}) = 0

x \to 0 - lim (x) = 0

= 0 + 0

Simplify

= 0

x \to 0 lim (\frac{8 sin ( 0 )}{0})

x + y = 3, y^{2} = 4 x, y = 0, 1

\int (sin^{2} (x) + cos (x))^{2} d x

f (x) = x - 2 sin (x)

\int_{0}^{2} \frac{x}{x ^{4} + 1} d x

What is the limit as x approaches 0-of (e^{2/x}*sin(pi(x)))/(x+2)+x ?
The limit as x approaches 0-of (e^{2/x}*sin(pi(x)))/(x+2)+x is 0