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I completely understand now! thank you so much for your help and clarity, I appreciate it!

sorry f' = (-(x+h) + (x+h) - (-x+x))/h = (-x - h + x + h + x - x)/h = 0/h not 2x/h

Yeah sorry for the confusion

Thanks for the replies! I fixed up the errors in my thread and added parentheses. so I re-did the left for x<0 I got f' = (-(x+h) + (x+h) - (-x+x))/h = (-x - h + x + h + x - x)/h = 2x/h but taking the limit as h->0 it is undefined is it an algebraic error I am making?

shouldn't f'(0) = 0 or undefined or dne since there is no derivative at 0?

also when I graph it out it only shows the right side / instead of V I don't understand how I got the left derivative as -1 when there's nothing on the left

So how do I show that mathematically? I understand that geometrically, but when I do problems like these I have a tough time doing it

Homework Statement f(x) = |x| + x Does f'(0) exist? Does f'(x) exist for values of x other than 0? This is from lang's a first course in calculus page 54 # 13 Homework Equations lim (f(x+h) - f(x))/h h->0 The Attempt at a Solution So I'm not sure if I am doing this...

Thank you! :)

Wow that's amazing. Thanks everyone! You are all wonderful

Would this be classified as a direct proof? I'm trying to learn proofs on my own so this is a little bit confusing to me. Thanks everyone for helping me out!

oh that just did it didn't it?!

so from this I got |a + b| <= |a| + |b| |(x+y) + (-y)| <= |x+y| + |-y| |x + y - y| <= |x+y| + |-y| |x| - |y| <= |x + y|

understandable no worries we all make mistakes!

okay so here is what I'm doing right now |x+y| >= |x| - |y| with x = x + y - y I got |x + y| >= |x| + |y| - |y| - |y| cancelling the |y| |x + y| >= |x| + |y| am I on the right track? :)

Thank you, I understand why x = x + y - y it is very obvious! I am confused because I have no idea what it has to do with the proof and where to apply it when proving that |x+y| >= |x| - |y|

I don't understand why I would write x + y ≥ x + y how does the subtraction turn into addition? does this mean that x + y = |x| - |y|? I see that -(-x) = + x but its |x| - |y| not |x| + |-y| or is my thinking wrong?

Homework Statement |x + y| ≥ |x| - |y| [Hint: write out x = x + y - y, and apply Theorem 3, together with the fact that |-y| = |y|] Homework Equations Theorem 3: |a + b| ≤ |a| + |b| x = x + y - y |-y| = |y| The Attempt at a Solution |x + y| ≥ |x| - |y| x = x + y - y (don't know where to...

You make it seem like becoming a professor is easy. You might as well have said, "I'm going to be famous by making the NHL or NBA or NFL, either that or I'm going to become a famous rapper or rock star or actor. Maybe all of the above...'' All jokes aside, you should consider teacher high...

I think you need to check your school and make sure its accredited. Where I am, engineering physics is one of the most difficult programs (UBC&SFU) and they are also accredited. Both these programs have a lot of computer eng/sci courses. UBC allows you to specialize in mech, electrical, compE...

Agreed. Perhaps he meant astronomy? I hope he meant astronomy.

Getting a degree for its own sake is ridiculously pointless. Think about what you want in life. It seems to me that you just want a degree, not even in something you have interest in, just an ''easier/faster'' route. If you really have a passion for astrophysics and you know your math skills are...

my mom always told me to just be myself!

Have you tried seeking professional help rather than asking random people on the internet who really don't know your situation or who don't have the right qualifications? I myself know nothing about bipolar so I really can't help much more. I think you would benefit a lot more from a...

I find the biggest problem is interest. If you are not interested in something, you will put it off and not want to do it. For example, in high school I hated school and just went to goof off with friends and play sports. Never did homework, failed math 11 twice even though I had a great tutor...

Whatever you heart desires :)

only some courses give out certificates of completion. I've taken many courses there for programming and math. They're great and free, i don't care much for the certificate. i think you are under the impression that these are credit courses which they are not. Universities will not look at...

Hello all, I will be starting university in September in physics(mathematical physics honours, its just a double major) but I have started to realize that I spend a lot more time on math then I do on physics. I have finished a few basic calculus books; Quick Calculus - Kleppner/ramsey, Calculus...

Whenever I do that I get excited because it looks intense :P I tell myself I'm going to be able to understand it soon. Then I start the book. Like micromass I like to start on page 1. But I do look ahead just to see what I will be learning

My mom cuts my hair so I don't have to worry :) But yes I have noticed that different barber cuts differently

Easily. I think you are too concerned about the mathematics required. For an introductory course in physics you use very little calculus. Unless you are using kleppner and kolenkow's book which actually requires thinking. The majority of students have never taken calculus before taking a first...

Do you have pictures

There's also Geophysics. Good money in it. Could always apply to law school or med school if your interested in that. I know many engineering grad schools which would accept physics bachelors. And medical physics like others have said.

Also to the OP. Many great contributions are made everyday be scientists all over the world. They can't all be geniuses now can they :P

I agree with your second paragraph completely. If you mean these great minds were geniuses as in they were extremely intelligent and creative, then I agree with you. The intelligence and creativity comes with years of practice and extremely hard work. Anyone can become intelligent and...

This. You are making this too big of a deal. Do what you love, forget about everything else. A lot of young people, including myself from time to time, think about these unnecessary things. No one is a genius, they either learned the necessary things at a younger age, or devote more time into...

Well first off you will not be generating income outside of grad school, it will be impossible to work full time, study, research, TA etc. Grad school usually keeps people very busy(from what I've heard its not impossible, just very unlikely). After getting your bachelors in physics you have...

Most people get a job :)

It was a different time back then my friend. If money is something you value greatly then I would suggest not going into science. You will be in school for 10+ years, get paid around 25 000/year +/- 10-20k depending what institution you are at for grad and post doc. So what I'm saying is...

you should ask yourself if its worth it all instead of others. If you think its worth it then i say go for it. you will never know unless you try. i think it is worth it for ME because this is what i want to do with my life and i believe that in life you have to give yourself the oppurtunity to...

Humans are not the only ones who have pets. i watched a documentary and a group of monkeys ( can't remember what kind or even if was monkeys or baboons or another animal it was awhile ago) found a dog and kept it as a pet. They played with the dog and didn't let it leave.

i don't understand what advice you want then. You specifically said "after a dual major in maths and applied maths" and "don't just tell me to major in physics/astrophysics". if you want to go into astrophysics the most logical route to take is a physics major or even a double major physics/math...

https://www.physicsforums.com/showthread.php?t=64966

Yes you will need better books like lebombo said. Take a look in the textbooks section. There are good books in there

I am in no position to give advice since I know nothing about prelim exams But I do have a suggestion. Maybe you can pick up some rigorous textbooks if you haven't already done so. I see spivak mentioned a lot and has quite the rep.

I can prefer classical music and instrumentals. Very calm music while I read or do physics. But only with no lyrics otherwise I started singing along and start thinking about the meaning behind the words. I can do math problems while listening to anything no problem though

no[its not too late]. its too early to tell anything. took myfirst physics course last year at 20 years old.

This

Just work hard at what you love. Simple. Forget all this useless worrying about iq and all that nonsense.

I don't really have to study for exams. I do review before but I do enough practice consistently to not have to cram.