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17h
comment $\lim_{x\to\infty}(\frac{x^2}{x^2+x})^x = 1 $ or $0$?
Neither. See mathlove's answer below for a serious hint
20h
comment Compute the following sum
I've added another step above. Now see what's going on? Notice that the 1/2 terms cancel. And the 1/3 terms. And the 1/4 terms ...
20h
revised Compute the following sum
added 177 characters in body
20h
answered Compute the following sum
20h
comment Compute the following sum
To make the hint more explicit: $$\frac{1}{n(n+1)} = \frac{1}{n} - \frac{1}{n+1}$$ See what to do now?
21h
comment If $f(x)=\sin^2(3-x)$, then what is $f'(0)?$
This is incorrect
21h
comment If $f(x)=\sin^2(3-x)$, then what is $f'(0)?$
Your answer is the same as option B, as $\sin 2x = 2\sin x \cos x$
1d
revised What is a basis for the vector space $ \Bbb{C}^{n} $ (a complex vector space)?
added 28 characters in body
1d
answered What is a basis for the vector space $ \Bbb{C}^{n} $ (a complex vector space)?
1d
reviewed Approve Find the value of: $\sum_{n=1}^{50}n(n!)$
2d
reviewed Close The riemann problem for p-system
2d
comment How can I simplify $\sqrt{3^2 + 3^2\tan^2\theta}$?
Certainly not correct. Is $\sqrt{a^2 + b^2} = ab$ in general? No. Ask instead: what is $1 + \tan^2\theta$ equal to?
2d
revised To find the minimum of $\int_0^1 (f''(x))^2dx$
deleted 35 characters in body
Apr
30
comment Regarding Peano's Axioms
S(0) is called "the number 1"; S(S(0)) is called "the number 2"; S(S(S(0))) is called "the number 3". What do you want to call S(S(S(S(0))))? We can call it whatever want ("Red lip gloss", ...). So I take it the intent of the Wikipedia comment is to say: suppose we have S applied some number of times to 0, what do we want to call that? Well, the common English definition of that number of times is as good a label as any. Those labels are completely arbitrary. What matters for the Peano axioms is that S(0) is distinct from S(S(0)), and both of those are distinct from S(S(S(0))). And so on.
Apr
30
comment Is the sum of the absolute value of the even terms in a Maclaurin Series greater than the sum of the odd terms?
Elegant, as usual
Apr
29
comment completeness definition
Convergent $\Rightarrow$ Cauchy regardless. Cauchy $\Rightarrow$ Convergent is the definition of what Complete means. So $(X,d)$ is complete iff all Cauchy sequences are convergent. See also what Brian just wrote.
Apr
29
comment completeness definition
All convergent series are Cauchy. If all Cauchy series are convergent then the metric space is by complete, by definition of that term.
Apr
29
comment ”lesser known” rules to calculate the derivative
Maybe a question for Mathematica SE
Apr
29
revised Especifying domain in expressions
added 249 characters in body
Apr
29
answered Especifying domain in expressions