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

The limit as x approaches 0 of (sin(xy))/x is y

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limit as x approaches 0 of (sin(xy))/x

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

y

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( x y ) y}{1})

= x \to 0 lim (\frac{cos ( x y ) y}{1})

Plug in the value

x = 0

= \frac{cos ( 0 \cdot y ) y}{1}

Simplify

\frac{cos ( 0 \cdot y ) y}{1} : y

= y

x \to 1 + lim (\frac{3 x}{x - 1})

x \to - 2 lim (\frac{∣ x ∣}{x})

x \to a lim (x + 4)

x \to 3 lim ((x + 3) (x - 5))

x \to 0 lim (\frac{2 sec ( x )}{csc ( x )})

What is the limit as x approaches 0 of (sin(xy))/x ?
The limit as x approaches 0 of (sin(xy))/x is y