The limit of Sin(xy)/x as (x,y) approaches (0,y) simplifies to y. This conclusion is reached by applying L'Hospital's rule, treating y as a constant during the differentiation process. The behavior of Sin(θ) for small values of θ also supports this result, confirming that the limit can be effectively evaluated using these mathematical techniques.
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trap101 said:So I figured out the solution to lim (x,y)-->(0,y) of Sin(xy)/x, but I figured it out by looking at a solution. I wanted to understand though why with respect to the above limit how Sin(xy)/x = y?
How do you separate the xy in the numerator?
Ray Vickson said:Use l'Hospitals's rule, or else look at the behavior of ##\sin \theta## for small ##|\theta|##.
trap101 said:Using L'Hospital's rule, would I essentially be treating "y" as a constant?