1 of 1MATH 241 S19HOMEWORKGiven that lim f(x) = -3, limg(r) = 2, and lim h(x) = 5, find 474 (a) [(r)6L+ (x)JzxJiuji (b) . lim(g(x) ~ xh(x)} [1 + g(x)l '(2) lim...

a. If $\lim _{x \rightarrow 2} \frac{f(x)-5}{x-2}=3,$ find $\lim _{x \rightarrow 2} f(x)$
b. If $\lim _{x \rightarrow 2} \frac{f(x)-5}{x-2}=4,$ find $\lim _{x \rightarrow 2} f(x)$

Hello. In this problem, we are given to limits. One is the limit of ever X finest five all over X minus toe a sex approach. Just tow. Be equal victory. And the other one is Leave it off. Fo X minus five. Oh, sorry. This is F of X minus, fighting all over X minus two. A sexy for just to a secret report and forget a lot. Then we have the boat equations, whereas we have ever x minus five for the numerator and X minus two. And then Denominator. And if we're gonna substitute to, will have ever toe minus five all over to minus two so that two minutes to is equal to zero. So the denominator surely will become syrup or boat. But how come we have a limit? Ignore. It happens when the party is indeterminate. Therefore the limit of X as except purchased should be equal five to make this limit in the terminating port. Because we're not sure what the function of X is And just know that it should be equal to five for this limits the work. So for leather A and B the answer. It's fire

Okay for this problem we've been given that the left side of the limits of some function is five and the right side. A limit of the same function is six. So what that says is if we kind of graft this? Ah, when we have exes to right here. Um, and let's have a height of five and six from the left. The function is gonna do something we don't know. It's gonna get up to two right here. It may be defined. It may not. And then from the right side, it's gonna jump to six. So this represents a jump, which means the limit does not exist. Thank you.

So for the first part, if we take a as to and G of X is equal to X turned minus three to the par five, then each of a will equal age of two, which would be cool to squared minus three, which is for Ryan Street is equal to one. We can then rewrite our limit function as H X minus H of to over X minus two for the second part. In order to use the change will we need to find the inner and outer function. So our inter function in this case is X squared minus three. And our outer function is you to the four or five. So do I write? The X is going to be the derivative of the outer function into the derivative of the inter function. And now we we'll substitute you into our equation, which is X squared minus three. And in order to get the limit when X goes to two, we put two into this equation. So we have 10 22 to a squared minus three to the power for jay equals 20

Hello. My name is Butler. And in this video we'll show her from the limit of dysfunction. So we have Y to the statue when 25 over Y plus five Is why tends to 95. So looking at this function, What would what would we normally do is plugging our -5 into the function. But here there's something which happens plugging five. If you plug in -5. So If you plug in -5, I hope you were gonna have minus wife with the poet. Chew my house device. All right. Minus five classified. And then what does this gives us? I'm still gonna talk even him someone the denominator. Now this is a problem country to answer it. Zoo. Zoo. So what do we do? What we do now is to introduce what we call the capitals. So what does limiters should say says that if you're finding the limit of a function. So every function on the numerator function again? The denominator. So these are functions of its and then we have vortex approaching a certain value. In this case she's a and if we get 0/0 or we forget infinity infinity then we can find the limits. I just first integrating the numerator and it was a integrate. Sorry to differentiate. Yes. So differentiate you married her and then also different shit. The denominator and then we still apply our limit. So this is what we're gonna do yet. So when a differentiated in America we also differentiate our dinner mediator. Great. So what's the derivative for narrator? You see that it's going to become two white. So five. It's just constant, which becomes zero and then Below year 1. 2 years. We have Why? Plus five. So you can have what? And then we apply our limit. That's why tends to make it chief. Why? Now we can plug in. So you two years negative. Five. Yeah. 21. And what does this gives us? This just gives us -10. So -10 becomes the limit. Thoughts of your of your function. Thank you for your time.