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Sep
5
answered How do I find the mass of a sphere using proportionality?
Sep
5
comment Analyse trigonometrical function
It looks as if you are only going $0$ to $2\pi$. That's OK if it was specified, otherwise you have to add $2n\pi$. Note that $\sin^3 x+\cos^3 x$ will only change sign where $\sin^3 x+\cos^3 x=0$. So it is positive until $\frac{3\pi}{4}$, then negative until $\frac{7\pi}{4}$, then positive up to $2\pi$.
Sep
4
revised Analyse trigonometrical function
deleted 208 characters in body
Sep
4
comment Analyse trigonometrical function
OK. Your comment does not ask a specific question.
Sep
4
comment The interest rate last year was 2%, this year it is 3% - did interest rates go up 1% or 50%
The normal mathematical interpretation is $50\%$. However, since there are a couple of interpretations, I would try to avoid the phrase. One could say in dollars how much interest you would be paying monthly on a loan, before and after.
Sep
4
answered Analyse trigonometrical function
Sep
4
answered Use the squeeze theorem to prove the convergence of a set
Sep
4
comment Find the Vertical Asymptotes for the function
The denominator is $(x+4)(x-2)$ and is $0$ at $-4$ and $2$. The numerator isn't. So the thing blows "up" as we approach $-4$ and as we approach $2$,
Sep
4
comment Why do you add +1 in counting test questions?
Use smaller numbers. How many numbers are there from $7$ to $10$ inclusive? There are $4$, you can list them. This is $1$ more than $10-7$.
Sep
4
answered Prove that $x^{1/n} > x^{1/(n+1)}$ given that $x>1$.
Sep
4
comment Cannot find the limit of this integral
There is something left for the OP to do. But the limit calculation is not difficult.
Sep
4
revised Probability that randomly chosen letters are both distinct and ordered
added 37 characters in body
Sep
4
answered Probability that randomly chosen letters are both distinct and ordered
Sep
4
comment Cannot find the limit of this integral
There are also fancy theorems one could quote, but I am guessing the course is an early one.
Sep
4
comment Cannot find the limit of this integral
Yes, the limit is $0$. If one has experience, it is obvious. Pick a small $\epsilon$. The integral from $\epsilon$ up goes to $0$, because $\frac{1}{x^n}$ shrinks rapidly. The integral from $1$ to $1+\epsilon$ is also small, because on this interval $\ln x$ is close to $0$.
Sep
4
revised Cannot find the limit of this integral
added 117 characters in body
Sep
4
comment Cannot find the limit of this integral
If you want slightly less ugly, you can use the fact that for $x\ge 1$, we have $0\le \ln x\le x-1$.
Sep
4
answered Cannot find the limit of this integral
Sep
4
comment Probability problem - Coin toss -
I was born in France.
Sep
4
comment Simple computational number theory
There are fancy algorithms, but for $2$ to $500$ you don't need fancy. For all $x$ from $1$ to $n-1$, check whether $x$ divides $n$. Keep a running total. You don't need to go to $n-1$, you can go to $\lfloor n/2\rfloor$.