What is the limit as x approaches 0 of (xe^x)/(sin(x)) ?

The limit as x approaches 0 of (xe^x)/(sin(x)) is 1

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limit as x approaches 0 of (xe^x)/(sin(x))

x \to 0 lim (\frac{x e ^{x}}{sin ( x )})

1

Solution steps

x \to 0 lim (\frac{x e ^{x}}{sin ( x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{e ^{x} + e ^{x} x}{cos ( x )})

Plug in the value

x = 0

= \frac{e ^{0} + e ^{0} \cdot 0}{cos ( 0 )}

Simplify

\frac{e ^{0} + e ^{0} \cdot 0}{cos ( 0 )} : 1

= 1

What is the limit as x approaches 0 of (xe^x)/(sin(x)) ?
The limit as x approaches 0 of (xe^x)/(sin(x)) is 1