For #1 I think you are doing great.
thank you. i really need the support and reassurance because... ow. and i'm pretty positive nobody at my house is able to help me because... yeah. calculus.
this really helped me out though!! i went to my professor's office hours (first time i've done that in college
) and since he just collected this he graded mine and i got a 48/50!! i went because another student asked him if they could do practice questions that modeled the ones that would be on our quiz today. between the two of us, i was the one who was understanding the concepts we were applying more
i think i did well on it... it was open note and book, though, AND i spent too much time trying to understand how to use a program i put on my calculator last night to find the volume of a sphere, BUT i found it after 15 minutes or so...
#2 are all "prove or disprove this" questions and they can be quite annoying
yea i hate these kind of questions
For (c): it's actually not true because for example y = sin(x) + 100x also have y'''' = sin(x)
this was the one he took two points off of because i didn't show the entire process of getting to the fourth derivative. but that's... that's whatever to me. i still got an a. he just wanted a little bit more.
For #3 I think you missed a y' as (4y^3*y')' = 12y^2 * y' * y' + 4y^3 * y'', not 12y^2 * y' + 4y^3 * y''
so it's y'' = (-12x^2-12y^2(y')^2)/(4y^3) = (-3x^2-3y^2(-x^3/y^3)^2)/(y^3) = (-3x^2-3y^2x^6/y^6)/(y^3) = (-3x^2-3x^4/y^4)/(y^3) = -3x^2(y^4 + x^4)/y^7
and since x^4 + y^4 = 16, so it's -3x^2(16)/y^7 = -48x^2/y^7
i think this is what genuinely helped the most. i had gone to my college's tutoring center for walk in tutoring to try and get this done (that's where i took the picture i posted) and the girl i talked to... i don't think she wasn't helpful, per say, but she's in higher level math courses and i could get forgetting what's taught in calc 1 when you've done multivariable calc. i've also just had a lot of trouble doing implicit differentiation and this helped me understand what the hell i'm supposed to be doing. although, i'm still getting used to reading and typing out math shit so i did have to google an ascii math converter to read this
I guess it's common to not feel confident enough when doing mathematical proof though, even professional mathematicians make mistake in papers
it's probably because i don't have a strong understanding of the subject yet, but some of the things you have to do to equations and numbers in calc seem impossible. it feels like fake math
but i'm working on it. it's cool as hell to me. i still can't believe i like math now but here we are
ANYWAYS. all that aside (can anyone tell that i'm my dad's kid by how much i write
) thank you for your help. i never thought i'd be able to do calculus, yet alone really be in college. i know a lot of my confusion can stem from me just... not knowing some of the basics. like when we were still just doing limits and we were dealing with delta epsilon problems?? :| i honestly still don't get those. but i don't know how often they'll really come up, so i'm... not too worried about it right now.