When evaluating limits, numbers approaching a value can come from both sides (less than or greater than), which can result in different outcomes; for example, 1/(x-1) approaches positive infinity when x approaches 1 from above, but negative infinity when x approaches 1 from below, demonstrating that limits must consider both directions of approach.
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Two Voices Solve This Calculus Problem in 1 Minute! | Mathy Daddy #shortsAdded:
Hey, want to tackle this limit problem real quick? Sure thing.
The answer they gave is infinity. Mhm, kind of right.
But remember that arrow means the number is getting closer to the value.
So here, XR is moving toward one. Oh, right. That's why I plugged in one. Then it's like one over zero.
If the denominator is zero, doesn't that just blow up to infinity?
I mean, so I was right then? Not exactly.
Here's the catch. Numbers approaching one can come from both sides.
Less than one or greater than one.
You only thought about numbers bigger than one. Oh, so like 0.99.
Exactly. If you plug in numbers less than one, the whole thing flips negative. That means it can go to negative infinity. Woah, so does that mean there are two answers? Ah, got it.
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