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Limlimx-(-1)- f(x) and x-(-l)+ flx)-0...

Question

Limlimx-(-1)- f(x) and x-(-l)+ flx)-0

lim lim x-(-1)- f(x) and x-(-l)+ flx) -0



Answers

$\lim _{x \rightarrow 0} x\left[\frac{1}{x}\right]$

Which is stated limit X approaches zero X minus motor effects and x minus J. Yeah. First cases X approaches zero minus. So it will will limit. Its approaches zero minus it's minus mode X minus six and x minus. This ability will be minus one. It will be just two kinds of X. Yeah. Fund it's less one differentiating the value will be Mhm. So because he wants to cool my L hospital through second case when it is zero plus, it will be x minus of X and downside. It will be it's minus. So I know where you will be zero. It is just zero X zero point zero plus. This will be exact. So I answered it will be you know, I Mhm. Mhm.

In this problem, let us rewrite our function effects. 1st Effects will be equal to minus X by X. My ex is less than 00 and X is equal to zero and this is X by X And access greater than zero. So this is nothing but -1 when X is less than zero zero and X is equal to zero and 1 if access Well, it depends. Now let us find the limit of fx home coming approaching X equals to zero from left hand side. Please. LTD fix coming from the left and saying this is nothing but minus one. And limit of effects X approaching from the right hand side is nothing but what? So we see that the left hand side limit on the right inside limited, you are not equal. Which means that limit fX extends to zero does not exists. That's all.

In this problem, let us rewrite our function F X. So the fix is nothing. But when X is less than zero, this is nothing but X upon minus X. Because when X is less than zero, mondex becomes minus X, This is equals to zero, A tax equal to zero and this is X upon X or X greater than zero. This is equivalent to -1 and ex is less than zero zero. When XS equals to zero and 1 My next is greater than zero. So let us find the left inside of the limit approaching effects From the negative side of zero. This is limit finding the left hand side of the limit. This is nothing but -1, unlimited. The right hand side of the limit is nothing but plus one. So we see that lift inside of the limit is not equal to right inside of the limit, which means that limit extends to zero. Fx does not exist. That's all.

In this moment, let us first find limited. FX extends to zero. Limit. Effects extends to see first let us find the left hand limit limit of ethics Extends to zero there's nothing but approaching from the left hand side, this takes the value of two and 20 plus three Which is equal. System three, That is all winter limit from the right hand side he will use the function three and two X plus one. So substituting X zero, this is three and 20 past one, which is one, which is so. So we see that would the limits approaching from the left hand side and the right inside is equal. So limit extends to zero. Ethics exists and it is equals 23 This party that this evaluate Limit extends to one Fx when so this is nothing but When X is approaching one from either direction, it fixes nothing but three and two X plus one. So this can be thought of as the value trying to express one assumes at X equals to one. So this is three into two, which is six. No


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