The limit of f(x) = 1/(x-1) as x approaches 1 does not exist because the left-hand limit approaches negative infinity while the right-hand limit approaches positive infinity, and these two values are not equal.
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1. Why This Limit Does NOT Exist 🤯 #calculus #limits #math #manim #mathematics #shorts #apcalculus追加:
f of x equals 1 / x - 1. This looks simple, but the behavior near x = 1 is very different. From the left, as x approaches 1, the denominator becomes a tiny negative number. So, f of x goes to negative infinity. From the right, the denominator becomes a tiny positive number. So, f of x goes to positive infinity. Negative infinity does not equal positive infinity. The left and right limits completely disagree.
Therefore, the limit does not exist, DNE.
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