What is the limit as x approaches 0+of sqrt(xe^{sin(pi/x))} ?

The limit as x approaches 0+of sqrt(xe^{sin(pi/x))} is 0

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limit as x approaches 0+of sqrt(xe^{sin(pi/x))}

x \to 0 + lim (x e^{s i n (\frac{π}{x})})

0

Solution steps

x \to 0 + lim (x e^{s i n (\frac{π}{x})})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= x \to 0 + lim (x e^{s i n (\frac{π}{x})})

Apply the Squeeze Theorem:

0

= 0

Simplify

= 0

sin (x) π

\int \frac{6 ln ^{2} ( x )}{x} d x

\int \frac{- 4 x}{( 1 - 2 x ^{2} ) ^{2}} d x

ln (\frac{1 + x}{1 - x}), 0

y^{^{'}} + x y^{2} = 0

What is the limit as x approaches 0+of sqrt(xe^{sin(pi/x))} ?
The limit as x approaches 0+of sqrt(xe^{sin(pi/x))} is 0