Thank you so much. Words cannot explain how relieved I am that I got this concept (finally!) my teacher took 50 minute and couldn't do it, and you did in less then 10 minutes from. You're great! I am definitely subscribing & learning calc from you!
Depends on what x approaches. If x approaches a value where the function splits apart, then you have to use one-sided limits. Two-sided limits won't work directly because the left side and right side will be different functions. (If you know that the two-sided limit exists and you're allowed to use that fact, then yes, that would be the answer.) But if you have something like in part d, with x approaching a value where the function doesn't split, then you can treat it like a two-sided limit.
I know. Looks like those should be "less than or equal to" in your F(x). Always look for the piece that's "just next to" the value x approaches. So if you want, e.g., the limit of F(x) as x approaches 2 from the right, just look at is the piece where F(x) = x+4, because this is the piece that is immediately to the right of x=2. There are other pieces, but since x goes to 2 from the right, then the piece where F(x) = x+4 is the last piece x is on before it would actually reach the value x=2.
I have a question, if anyone could pls answer huhu if the -9 from letter d was coming from the right instead of left, would u still use the same equation?? Coz if it's coming from the right of - 9, wont there be numbers >6?? Thank u in advance:)
There are numbers > 6, but with limits we only care about what is happening "really really close" to the limit point. As x gets closer and closer to -9, x will eventually become less than 6, so we don't care what happens when x > 6. When x is "really really close" to -9 we will be on the piece where f(x) is x+2.
I just used "less than or equal" since that's the type of inequality used in the piecewise function definition. It's true that x is never actually equal to 6. If you want, you can replace the logic in the explanation with just plain "less than" and it'll still work. More generally though, if x is always less than 6 and is never equal to 6, it's still correct to say "x is less than or equal to 6."
Thanks. Yes, it doesn't come from anywhere, it's just the number I chose to use for that example. It's like asking where f came from - it's just what I chose to use.
This video doesn't take into account that there might be more than two functions that you might be able to plug in. For example F(x)= {-x-2, -infinity < x
Also want to mention again (it's covered in an earlier video) that when x approaches a value in a limit, x never actually equals that value. It just keeps getting closer and closer, but never actually hits the value. That's why I said "would actually reach the value" and not "reaches the value" in the comment above. Just a small detail worth pointing out again Anyway, can do some examples like that in a separate video.
It's true that x is not equal to 6 but that doesn't matter. Part b is the limit from the right-hand side only. Therefore we evaluate the limit using the branch where x is greater than 6. It is actually incorrect to use the other branch precisely because x is greater than 6.
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Thank you so much. Words cannot explain how relieved I am that I got this concept (finally!) my teacher took 50 minute and couldn't do it, and you did in less then 10 minutes from. You're great! I am definitely subscribing & learning calc from you!
Thanks so much, idk who the hell would dislike this, it was clear and concise
i was stuck on my calc hw because my teacher didn't go over this, but you made it clear now. thanks!
you teach better than my maths teacher , thanks a lot !!!!!!!!!!!
you saved me as well . Huge thanks for putting it in Layman's terms
when i watched this video .I easily solves question ..
i am very very Thank full of You
Depends on what x approaches. If x approaches a value where the function splits apart, then you have to use one-sided limits. Two-sided limits won't work directly because the left side and right side will be different functions. (If you know that the two-sided limit exists and you're allowed to use that fact, then yes, that would be the answer.)
But if you have something like in part d, with x approaching a value where the function doesn't split, then you can treat it like a two-sided limit.
thank you lord math tutorials are born!
dude thank you so much man. PreCalc final in two days
This video helped me get through my homework. Thanks!
High quality video.
Thank you for your time and effort.
God bless u for making this excellent video!
Thanks! this is a lot faster than finding the limit from the graph
nice and clear
Dont stop making videos please!
I know this is old but...THANK YOU!!! I finally understand!!!!!
mid terms tmrow and u saved my life
ty :)
This was extremely helpful!! thanks so much!
I know. Looks like those should be "less than or equal to" in your F(x).
Always look for the piece that's "just next to" the value x approaches. So if you want, e.g., the limit of F(x) as x approaches 2 from the right, just look at is the piece where F(x) = x+4, because this is the piece that is immediately to the right of x=2. There are other pieces, but since x goes to 2 from the right, then the piece where F(x) = x+4 is the last piece x is on before it would actually reach the value x=2.
Thanks man!!! It was really helpful.
Thanks, glad to help.
never had any pre calculus dayz Just calculus.
The -9 in part d? Nowhere. It's just the number I randomly chose to use in that example.
thank you so muchhhh!!! saved me 😭😆
The video sound is pretty good, beyond my imagination
This was so helpful
You, are awesome. Thank you!!!
very helpful...you're the man
What if the two sided limit does exist? Is it just that answer or is there more work needed to be done?
omg thank you sooo much. you are a God send
And you. Glad to help.
short and simple. thanks a lot.
Thanks! Helped me a lot.
Can you see it as if negative side smaller that positive it makes less than
.You're a god!
what do you do if your given a piecewise function, but your limit is infinity?
Thank you for posting this video :-)
Awesome video helped alot!!!!1
Character In the video It's great, I like it a lot $$
How do i solve if the two-sided limit exists?
thank you so much!!
Thank you so much
'so the function is discontinues at x=6 right?
Haha, thanks, glad to help.
Sir can I message you I really need help. For my test
excellent 😍
I have a question, if anyone could pls answer huhu if the -9 from letter d was coming from the right instead of left, would u still use the same equation?? Coz if it's coming from the right of - 9, wont there be numbers >6?? Thank u in advance:)
There are numbers > 6, but with limits we only care about what is happening "really really close" to the limit point. As x gets closer and closer to -9, x will eventually become less than 6, so we don't care what happens when x > 6. When x is "really really close" to -9 we will be on the piece where f(x) is x+2.
i dont get it, in the limits we dont use equality because the x approaches not exactly equal, so how come we used the "less or equal to six"
I just used "less than or equal" since that's the type of inequality used in the piecewise function definition. It's true that x is never actually equal to 6. If you want, you can replace the logic in the explanation with just plain "less than" and it'll still work. More generally though, if x is always less than 6 and is never equal to 6, it's still correct to say "x is less than or equal to 6."
ooh alright,, thank you for the explanation 👍🏽
great video...just confused where you got the -9 from
It's just an additional example.
Thanks. Yes, it doesn't come from anywhere, it's just the number I chose to use for that example. It's like asking where f came from - it's just what I chose to use.
that was amazing thanks! saved my ass for my midterm!
Wonderful
Thank you.
looks like im passing my first test of the semester tomorow... hopefully lol
The function is discontinuous at x=6 but I didn't mention it in the video since I didn't start talking about continuity until a later video.
Wow thank you!!!!
This video doesn't take into account that there might be more than two functions that you might be able to plug in.
For example
F(x)=
{-x-2, -infinity < x
Also want to mention again (it's covered in an earlier video) that when x approaches a value in a limit, x never actually equals that value. It just keeps getting closer and closer, but never actually hits the value. That's why I said "would actually reach the value" and not "reaches the value" in the comment above. Just a small detail worth pointing out again
Anyway, can do some examples like that in a separate video.
thank you Sir
thank you!
Bless up.
Ty
God bless you -333
a lot of thanks :
thanks a lot
Wait...where'd you pull -9 from?
Thanks!!!!
What if x tends 0
I mean x≤0 and x>0
Thanks
If only my math teacher could explain things like this... or even explain things at all 🙄🙄
this video is sooooooooooo....................... helpful. tank U4 posting it.
thank
Nice
nice!
Thanks bruh
awesome
salute
I think you have made a mistake whan you do B.
Because x is greater than 6 that means not equal to 6
It's true that x is not equal to 6 but that doesn't matter. Part b is the limit from the right-hand side only. Therefore we evaluate the limit using the branch where x is greater than 6. It is actually incorrect to use the other branch precisely because x is greater than 6.
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Dylan Quinones-Mattei
shutcho dylan matty headass up
He filming with his microwave
Wow this helped a lot. Thank you.
The video sound is pretty good, beyond my imagination
thank you!