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The limit of the product of a function and a constant is equal to the limit of the function, times the constant. For example: $\displaystyle\lim_{t\to 0}{\left(\frac{t}{2}\right)}=\lim_{t\to 0}{\left(\frac{1}{2}t\right)}=\frac{1}{2}\cdot\lim_{t\to 0}{\left(t\right)}$
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$x\frac{1}{x}\lim_{y\to0}\left(\frac{\sin\left(xy\right)}{y}\right)$
Learn how to solve limits problems step by step online. Find the limit x((y)->(0)lim(sin(xy)/(yx))). The limit of the product of a function and a constant is equal to the limit of the function, times the constant. For example: \displaystyle\lim_{t\to 0}{\left(\frac{t}{2}\right)}=\lim_{t\to 0}{\left(\frac{1}{2}t\right)}=\frac{1}{2}\cdot\lim_{t\to 0}{\left(t\right)}. Multiply the fraction and term. Simplify the fraction . If we directly evaluate the limit \lim_{y\to 0}\left(\frac{\sin\left(xy\right)}{y}\right) as y tends to 0, we can see that it gives us an indeterminate form.