Problem: https://gyazo.com/e7139a8c9fc2926cabd123a18f22f226
I have this problem and I know the limit is zero. I can also prove it with the squeeze theorem. The issue I have is it says to use the definition of limits so do I need to solve it another way and how woud I go about doing that? The definitions confuse me a little bit.
I'm asked to describe how to use the precise definition to prove limit statements. I'm not sure how to word it.
I'm using Stewart's Calculus to try to figure out the precise definition of a limit, but his explanation feels needlessly complicated and roundabout. I've been trying to work through it for the past two hours but it honestly feels he half-assed the explanation.
How did you guys learn this concept and did any online resources/textbook provide a better explanation?
resolved: just watched a crap ton of youtube videos. calc textbook sucks
Definitions give us a way to validate the "existence" of things and they are convenient but we have to be wary of using definitions for they also constrain and restrict the things true potential
Really refreshing to play with a wider range of cards and the guild flavors really add to the event. Would love to see these more often, well done!
Hi guys, I’ve been struggling the whole day with this one proof. The function is f(x)=9. The limit is lim x->a ( f(x) ) = 9, where a is any real number. I have to use epsilon-delta definition to prove the limit.
My scratchwork so far has only led me to the conclusion that |x-9| < delta, given the eighth limit law which states lim x->a (x) = a.
I’ve racked my brain trying to figure out how the hell I can even prove this since it seems as though epsilon equals zero. There must be something I missed in my lessons because my notes have nothing on this, nor do the homework assignments I’ve done. Any and all help is appreciated.
I thought I had it but I ran into some trouble on some homework. I found a site that was spelling it out really simply, until they reached the part about the rectangle.
- How does it cause a bigger gap between the two halves of the function? I don't get that at all.
- Why is |x - c|< delta not true at the hole (when x = c?) Wouldn't that just imply 0 < delta? If delta is positive, how is 0 not less than delta?
Is there a really good textbook/YouTube channel/website that will help me get this inside out? Cause I'm going to need to use it to prove some of the limit properties but it's all starting to seem like gibberish the more i look at it.😕
Have you ever seen the limit definition of higher derivatives of a function? For example, the second derivative of a function f(x) can be written as lim(h→0)[f(x+2h)-2f(x+h)+f(x)]/h² and the third derivative can be written as lim(h→0)[f(x+3h)-3f(x+2h)+3f(x+h)-f(x)]/h³. Wondering why the binomial coefficients are turning up here? Check out this video to find out! https://youtu.be/s_MRzW1Ckhk
Let me know if you have questions (or opinions in general) about the content!
I would like to practice finding limits \ the right epsilon\delta, but I couldn't find fitting problems in the sidebar.
any sources?
Come on guys! It's a Dead Giveaway!
How do you define yourself?
By your title within your family? By how many friends you have? By your relationship status? By your gender? By your job? By how much money you have? By what you’ve done? By what’s happened to you? By some label you or someone placed on you? By some dis-ease or health problem? By your capabilities or in capabilities?
There’s a million different labels and ways us humans choose to define who we are. And now I’m asking you, why do we feel the need to define ourselves if definitions are limited by nature? What would happen if we weren’t always putting ourselves in some sort of box or stagnant title?
I used to do this. I was consumed by labels. I thought this is who I am. I’m a daughter, I don’t have many friends, I’m in a relationship, I’m a woman. I’m an accountant... etc. but these things do not define me. Whenever I’ve clung to a label and one day that label went away or transformed into the opposite, I didn’t know what to do. I was completely lost because I had defined myself on outer terms that are forever changing. And I limited myself, “oh I can’t do that, I’m a girl,” or “I’m broken because my Dad died when I was young”, or “bad things have happened to me and that means that bad things will always happen.” These are real limiting beliefs all based in illusions. I was fixated on them. And then I thought, who am I underneath all of these? What would my life look like if I chose to understand I have value and I am not defined by anything on the outside?
I still work on it everyday because old habitual thought patterns are subconscious and need lots of healing but once an illusion is shattered it doesn’t ever come back in the same form. We are not any label. We are so much more and to define ourselves by one thing or another is so limiting. We are truly capable of things beyond measure and I’ve found labels only hold me back from achieving the things I want to achieve. Today is a new day. We don’t have to be the same that we were yesterday, we can choose to move beyond and do better. Move beyond the labels. Move beyond the limits. What lies beyond them is nothing short of magic.
if you don't believe me just try to look it up, I dare you
"Oh, it was nothing."
Addictionary!
 definition of limit)