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bio website xuanji.appspot.com
location Singapore
age 21
visits member for 3 years
seen Dec 9 at 0:07

Student


Sep
30
awarded  Explainer
Jan
19
answered Mathematically, why does $[ma]\mathrm{d}x = [mv]\mathrm{d}v$?
Sep
25
revised Why is integral of $(\tan x)^3$ not $((\sec x)^2)/2 - \ln(\sec x)$?
add latex formatting
Sep
25
suggested approved edit on Why is integral of $(\tan x)^3$ not $((\sec x)^2)/2 - \ln(\sec x)$?
Sep
24
comment L'Hopsital Rule Understanding
let us continue this discussion in chat
Sep
24
comment L'Hopsital Rule Understanding
That's not true, $f'/g'$ might be undefined while $\lim f'/g'$ exists.
Sep
24
comment L'Hopsital Rule Understanding
Fair enough. But why doesn't your answer point out this limitation of your proof? I can comment on your answer instead if you want.
Sep
24
comment L'Hopsital Rule Understanding
I think any proof or proof intuition for l'Hopital's rule must be roughly as complex as mine. Your proof shows that $\lim f/g = f'/g'$, but l'Hopital's rule is that $\lim f/g = \lim f'/g'$. The later is much harder to prove than the former. In fact, I think you should point out this limitation in your answer
Sep
24
comment L'Hopsital Rule Understanding
Your proof doesn't work for applying l'Hopital's rule twice, your final expression is a ratio of derivatives without a limit in front.
Sep
24
comment L'Hopsital Rule Understanding
Because if you apply l'Hopital's rule twice, you are eliminating the zeroth and first order terms, and focusing on the quadratic terms of the functions
Sep
24
comment L'Hopsital Rule Understanding
then you need to talk about quadratic, cubic, quartic...etc approximations. I know the proof of taylor's theorem isn't very simple, but I find the fact that any nice function has a first, second, etc order approximation to be self-evident
Sep
24
comment L'Hopsital Rule Understanding
I know, this is how I express the intuition that "the first-order term determines the limit" which I think of when using l'Hopital's rule.
Sep
24
answered L'Hopsital Rule Understanding
Sep
24
revised L'Hopsital Rule Understanding
add latex formatting
Sep
24
suggested approved edit on L'Hopsital Rule Understanding
Sep
23
comment Show that $\gcd(a,b)=\operatorname{lcm}(a,b)$ if and only if $a=b$.
I'm sure this will work, but sometimes these results about gcd and lcm are used as lemmas to prove the fundamental theorem of arithmetic
Sep
23
awarded  Critic
Sep
23
comment Show that $\gcd(a,b)=\operatorname{lcm}(a,b)$ if and only if $a=b$.
What are you allowed to assume? For example, if you are allowed to use the fact that every number has a unique prime factorization, then the proof is almost trivial (if it still isn't, I can write it as an answer)
Sep
23
revised To what extent are divisibility by different primes independent?
replace \mod by \pmod and remove brackets
Sep
23
comment Role of 1 in homogeneous transformation matrices
If 1 is replaced by $s$, the last row of $Tx$ will be $s$, but our convention is that a "represented vector" has 1 as its last element. Btw, it is a bit distracting to read what you write if you don't use latex.