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scope and limits

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does anybody know the scope and limits of the general equation to find the tangent to a curve at the point(xo,yo)
the equation is the following:

y-yo=dy/dx(x-xo)

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i think you have to show a test of possible values for xo and yo using different types of numbers (i.e. integers, rational numbers, irrational numbers etc.) and from there the kinds of numbers that don't work in the equation are the ones you discuss in the limits and scope
when i did my portfolio i set my tests up in a chart
hope that helped ;)

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