1 lim Etan Is D4 360 [email protected] b 3 9 2 BFI...

$\lim _{x \rightarrow 1} \frac{3 x^{2}-4 x+1}{x^{2}-1}$ is (a) 0 (b) 1 (c) $-1$ (d) 2

So We have our number 124 in which we need to elevate limit Limit X approaches to one. X approaches to one. Three X squared minus four X plus one. three x esquire -4 x plus one divided by x squared minus one, X squared minus one. This means limit X approaches to one And if we just characterize it it will become three x esquire minus. Okay, okay three extra Squire. This is four and 123 So four into when You should be minus four X -3 X -3, X minus X plus one, divide by access square minus when So limit x approaches to one. If we take three X. S comment It will be X -3 -1, X minus four X and three. Okay It should be X -1 & X -1 divided by X plus one in two, X minus one limit X approaches to one X -1 in two, 3, -1, divided by x plus one into x minus one. These two cancel out no if we are approaching X towards one, so this will be three minus 12 by two, which is one, so one should be the great dancer and option number B is the correct choice. Thank you.

To hear. We need to find out limit extent to buy battery off. Yes, course X plus by basics Divided by 1 -2 But made to 192. Cossacks to the power to buy three. Okay so we need to find out this limit so this can be written as so before that here will substitute there is equal to x minus biometric. Okay well substitute is X minus paper tree. Therefore limit will become limit extends to buy battery off Cameed by their 2-. Sorry pi beta plus dessert divided by 1 -2 costs. Bye Bye. three plus. Is there All to the power to buy three. Okay so when we substitute That is equal explains 583 will get this limit that is this is equal to limit. So here when we substitute one thing we need to be careful. The limited change that is when we substitute this will become that tends to zero because we have already substituted. Yes That tends to zero. So here if you look at the numerator this in the form of course 90 minus theta. Course 90 minus 30 is nothing but negative sign data Divided by the denominator will become one cozy plus road three ST C to the power to better that is this limit will become limit That 10 0 off. So scientific and bitterness to sign database cause databases that is two signs that by two Cause that by two and similarly from the denominator Bulgak sign that by two To about three beta common kendo Zeins that by two plus road trained Cause that by two older the both rebate thirties limit will become a limit zero and 20 off -2 to the power one by train. Zain, zebra two To the power one x 1 x three and the because that they took cultivated by Then. That by two plus road terrain Because that by two all to the power to better now we will apply the limit that is as that tends to zero. This will become century B zero And cause there will be one and similarly in the numerator also say that is our limit will welcome -2 to about one x 3. Window zero into one divided by road trip. To the power To battery. That is nothing but zero. This is the value of the limit and hence options to use the great answer.

So here were given a limit that is limited extends to be able to of one minus. Can expect to into one minus sine X divided by one plus tonics by two, hindu By -2 x. The old So we need to find out the value of the Islamic. Okay so here will directly play the hospitals. That is a playing in hospitals throw this limit can be written as limit extends to buy beto. Oh standby before minus expert took in the one minus sine X divided by according to buy before minus X. Beto In the five minutes to X the whole Cube. Sorry whole square that is This limit will become limited. He extends to buy before sorry It will become it will be the next inspired by two and this all of them will reduce to -6 divided by eight into negative too In two x -2. works okay that is this is nothing but limit. Excellent bite off that is in all the all the terms. So here also this will be 0x0 Here also this will be 0x0. So we took the liberty of this so we got this. Now again we need to get take the derivative so it will be -6 divided by 16 into minus two. That is now we will apply the limit so denominator will be negative 3030 32 and negative negative will get cancelled. 32 divided by Has extends to bye bye to this will become one. This is the value of the limit and hence option cst they dance it

Hello, everyone. I hope all is well today. I'll be helping you with the 10th problem, which is, as the limit of X goes to infinity up three x to the third minus seven X squared plus two over for X squared minus three X minus one. Um, what is it equal? So we're trying to find what the sequels. And for those of you who are not in calculus, I would approach this by inputting ah three x to the third minus for X squared plus two. So and the, uh um calculator in put it like this. So that's how it in put it. And then that would be multiplied by four X squared minus three X minus one. So then, once I was in there, I would enter table set and set the table set to 1 10 and then the table to 10 entered the table and scroll down to the larger and larger X values until you're convinced that why one grows without bound. Okay, so and then for you. For those of you who are in calculus, what I do is that divide everything. So I literally divide this whole entire thing. So I'm divide this whole entire thing by Sorry. Uh um, let me erase the equal sign. So what I would do is I take this whole entire thing and I'm divided by X to the third because it would be going down by the biggest, um, power. So then we'd be left with limit of X as it approaches. Infinity of three minus seven over X plus two over four, over X minus three over X squared plus two over X to the third, um, And then the numerator approaches three while the denominator approaches zero. So the whole fracturing grows without bound. Because when you plug this in, this would equal zero. This would equal zero. This would equal zero, and then, um, this would be divided by extra third, but these two would also grow to zero. So just be three over zero, so grow without bound. So that was why it is e infinity. So I hope you found it helpful. And I hope you have a great day. Thank you.