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Calculemus
  • Member for 9 years, 4 months
  • Last seen more than a month ago
  • Canada
6 votes
1 answer
86 views

Calculating $H'(x)$ given $H(x) = \int_{x^3 + 1}^{x^2 + 2x} e^{-t^2} dt$

5 votes
2 answers
7k views

Can someone explain this proof of the product property of square roots?

5 votes
5 answers
823 views

Why isn't the definition of absolute value applied when squaring a radical containing a variable?

5 votes
2 answers
223 views

What is the range of this combined function?

5 votes
1 answer
2k views

Can I say "if a sequence is not bounded above, then it is divergent to positive infinity" without explicitly saying it's eventually increasing?

4 votes
1 answer
104 views

How do we express "$\int_a^\infty f(x) \, dx$ is convergent" using predicate logic?

4 votes
2 answers
508 views

Can we have normal vectors to a plane that do not start at the origin?

3 votes
4 answers
56 views

When proving that every convergent sequence is bounded, do we have to fix $\epsilon$ to a concrete number in the proof, or can we let it be arbitrary?

3 votes
3 answers
476 views

Why can't we assume $0 < |x - a| \leq \delta$ (equality) in an epsilon delta proof?

2 votes
3 answers
244 views

How is $\lim_{x \to 0} \frac{\sin x}{x} = 1$ used to compute $\lim_{x \to 0} \frac{\sin 2x}{x}$?

2 votes
2 answers
55 views

What's it called when, in a proof, we define a new variable/function in terms of two existing ones, in order to make it easier to write or follow?

2 votes
1 answer
2k views

Side limits of a function with a cusp (does the limit exist at the cusp? is it it differentiable at the cusp?)

2 votes
1 answer
146 views

Quantifying a free variable in an example from "How To Prove It" by Velleman

2 votes
3 answers
259 views

Logic: "the cubic root of a rational number is also a rational number"

2 votes
1 answer
140 views

Does closure property work in reverse? That is, if $a + b$ belongs to a set closed under addition, are $a$ and $b$ members of that set?

2 votes
1 answer
100 views

Quantifying a variable in a set after specifying the set

2 votes
1 answer
162 views

Given this definition of the vector form of a line, why are some of the highlighted statements not acceptable as a shorthand?

2 votes
1 answer
89 views

Does $f$ have to be a continuous function in the definition for an improper integral of an unbounded function?

2 votes
3 answers
103 views

Proving $\lim\limits_{n \to \infty} \frac{n^a}{c^n} = 0$ using L'Hôpital's Rule

2 votes
0 answers
70 views

Computing $\int_{-1}^1 \frac{1}{x^2} dx$ (improper integral)

2 votes
4 answers
147 views

Integrating $\int \frac{dx}{\sqrt{x} (1 + x^2)}$

2 votes
3 answers
197 views

Why are the extremes of integration considered values of $x$ when computing an integral by substitution?

2 votes
2 answers
5k views

Do one-dimensional vectors exist? What are they used for?

2 votes
4 answers
90 views

Can someone explain this proof that $\text{span} \{ \vec u, \vec v \} = \text{span} \{ \vec u, \vec v, \vec w \}$?

1 vote
2 answers
226 views

How do we construct a continuous function on the interval $(0, 1]$ without a minimum or a maximum?

1 vote
4 answers
117 views

Finding $\int \sec^2 x \tan x \, dx$, I get $\frac12\sec^2x+C$, but an online calculator gets $\frac12\tan^2x+C$.

1 vote
4 answers
101 views

The sequence $\left\{ \frac{5}{n} \right\}_{n=1}^\infty$ is not monotonic, or not convergent, or bounded. Why?

1 vote
1 answer
37 views

Is this Change of Variable Theorem fine as it is, or should we specify the domain that $f$ is continuous on?

1 vote
1 answer
40 views

How was row reduction used to obtain the result in this example?

1 vote
1 answer
292 views

How does modulo operation work in terms of the remainder of long division with negative dividends?