WEBVTT
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we want to find values of A and B for
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the following limit as experts zero. That makes it
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equal to zero. So if we want this to
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be true, well, first, let's go ahead
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and just simplify this a little bit. So the
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first thing we can do is distributed across the pluses
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, and really, I'll just go ahead and group
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it like this to start. So the limit as
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X approaches zero, uh, sign of two x
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over execute. And actually, I'll go ahead and
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combined these two just by adding them really quickly.
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So in the new mirror, that's gonna be a
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plus B X all over, and then we'll have
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the x cute. So we'll have that and will
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have plus the limit as ex approach zero of a
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0 to 0. And we know that a is
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a constant with respect to X. So this year
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will just end up being a so we can go
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ahead and some truck that over and so will get
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negative. A is equal to the limit as X
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approaches zero of signed to X plus bx over x
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cute. So we have this now. Now,
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if we were to just plug this in directly.
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Well, we're going to have zero. They're zero
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. They're enduring the denominator. So we have zero
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over zero, which means we can imply low petals
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rule to this. So for this next up,
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we're going to apply Loki tolls. And so that's
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going to give us. That's the limit. As
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X approaches zero of what the derivative of sign is
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co sign to X, and then we have to
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apply chain rules that we take the drone on the
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inside. So you multiply that by two, and
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then we take the derivative of B X, which
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just leaves us with B and then in the denominator
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will have three x squared. And this year should
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still be equal to negative, eh? Okay,
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Now, if we were to apply the limit directly
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, so co sign of zero is one. So
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, Wendell, with two plus b and then the
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denominator, we end up with zero. So we
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still can't divide by zero. But we want this
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limit toe hold. So that means So this implies
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we want our numerator toe also be zero. So
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we're gonna want to plus B to be equal to
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zero, which implies B is equal to negative too
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. So we found one value. So I'm just
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gonna go ahead and put that up here at the
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start. So B is equal to two, and
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now we can go ahead and plug that in for
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B. And doing that will give us something that
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we can take the derivative with respect to Earth.
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Apply low petals rule. Since, what? Zero
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over zero. So I'll just go ahead and apply
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Loki tall to walk in. So that's going to
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be the limit as X approaches zero of So we're
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going to have too. So the derivative of co
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sign is going to be negative. Sign to X
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, and then we have that, too, on
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inside that we have to take the derivative look that
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out front. So this too would actually become a
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four. And then we divide this by so we'd
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get X. And then we have to move that
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too out front by power room. And so then
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we'd get two times three or six. Okay.
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No, If we were to apply the lead here
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again, Sign of zero is gonna be zero X
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is just going to be zero. So we can
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imply. Loki told you one more time and I'll
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go ahead and move this up here. So by
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Loki tolls rule again. And actually, one thing
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I should still have over here is that the right
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hand side of our equation should still be equal to
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negative eight. Yeah. So now, using low
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petals ruled, the left hand side is going to
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become the limit as Ex purchase zero. Oh,
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so we take the derivative of the numerator again.
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So the derivative of sign is going to be co
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side to X. Then we have to take the
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derivative of change rule. So we end up with
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another two, multiply that by the negative for we
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already had that becomes negative eight and then in the
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denominator, the derivative of six X, which is
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be six. And this here is still equal to
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negative. Now we can go ahead and applied the
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limit again and again. Co sign of zero is
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going to be one. So we'll end up with
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negative eight over six. Busy, eh? Are
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negative, eh? So we could multiply the negative
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over and simplify it over six to give us 4/3
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. So we end up with that. A is
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equal to 4/3 and B is equal to negative too
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.