I am trying to graph the function f(x)=xcotx.
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Usually we find the y-intercept by plugging in x=0. However, this is an undefined point because it involves division by zero. We need to consider the limits as x approaches zero from the negative side and from the positive side. If these limits are the same we have the limit as x→0. When x is very small, tan(x)≈x, so the limit is x/x=1, because xcot(x)=x/tan(x). This makes the y-intercept effectively (0,1) even though this point is actually undefined. The graph appears to intercept the y-axis at (0,1).

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