Tagged Questions
3
votes
2answers
48 views
Separating $\frac{1}{1-x^2}$ into multiple terms
I'm working through an example that contains the following steps:
$$\int\frac{1}{1-x^2}dx$$
$$=\frac{1}{2}\int\frac{1}{1+x} - \frac{1}{1-x}dx$$
$$\ldots$$
$$=\frac{1}{2}\ln{\frac{1+x}{1-x}}$$
I ...
4
votes
4answers
190 views
Of all the possible combinations of positive numbers that sum to 10, which has the largest multiplication?
Of all the possible combinations of positive numbers that sum to 10, which has the largest multiplication?
I had also got a clue: it's related to e.
Please help! ...
1
vote
2answers
155 views
How does he get a perfect swap numerator and denominator.
I'm going through a exercise, in which all the answers are given, but the tutor makes a step and I can't follow at all. A massive jump with no explanation.
Here is the question:
$\lim_{x \to 2} ...
1
vote
1answer
77 views
Looking for hints of this inequality
I think the following two inequalities are true. However, the proof may not be easy. Does anyone have any hints? Thank you very much!
Fix $a>1$. there exists two constants $K_1$ and $K_2$, such ...
5
votes
2answers
253 views
Evaluate fraction of sum
So i have to evaluate this sum:
$\displaystyle \frac{1-2^{-2}+4^{-2}-5^{-2}+7^{-2}-8^{-2}+10^{-2}-11^{-2}+\cdots}{1+2^{-2}-4^{-2}-5^{-2}+7^{-2}+8^{-2}-10^{-2}-11^{-2}+\cdots}$
it has the form :
...
0
votes
0answers
94 views
General advice for dividing bigger fraction into partial fractions
There's a lot of cases where dividing a larger fraction into smaller ones helps a lot in making calculations a lot simpler. For example, the first step in solving this integral below is to divide ...
