Prove by induction that for all $n$, $8$ is a factor of $7^{2n+1} +1$
I want to prove by induction that for all $n$, 8 is a factor of $$7^{2n+1}+1$$ I have proved it true for the base case and assumed it true for $n=k$, but ...
Apr 21, 2026 2 VIEWS
Topic: General
5104 Articles 
Finding the general solution of the differential equation $y' = xy$
Find the general solution of the differential equation: $y' = xy$. Disagreeing with my friend on this, what's your take?
Apr 21, 2026 2 VIEWS
What is the difference between $\arg(z)$ and $\operatorname{Arg}(z)$, where $z=a+bi$
What is the difference between the $\arg(z)$ and the $\operatorname{Arg}(z)$, where $z$ is a complex number of the form $a+bi$, for example: $z = -2 - 2i$...
Apr 21, 2026 1 VIEWS
Is there a method to figure out how many decimal places there are for a recurring decimal?
For example, like for 1/7 = 0.14285714285. 142857 is repeated in this recurring decimal, and those 6 decimal places are repeated. So is there a method to ...
Apr 21, 2026 1 VIEWS
How can you normalize two data sets to the same scale?
I have two data sets, one that ranges from 0-200, and another that ranges from ~400-~2500. I would like to compare the two according to a score from 0-10....
Apr 21, 2026 1 VIEWS
How to simplify $\frac{18}{\sqrt{162}}$
How to simplify $\frac{18}{\sqrt{162}}$? I tried and got $\frac{2}{\sqrt{2}}$ which is wrong?
Apr 21, 2026 1 VIEWS
how many distinct real zeros a function has
$f(x)= x^4+2x^3-2x^2+1$ How many distinct real zeroes does $f$ have? Is it two because it crosses the $x$-axis twice or am I completely wrong?
Apr 21, 2026 1 VIEWS
Antiderivative of $3\cos(x^3)\sin{x}$
I am practicing for an exam by randomly picking an expression to anti-differentiate when I came up with this one: $3\cos(x^3)\sin{x}$ . How would I go abo...
Apr 21, 2026 1 VIEWS
Greatest Integer function limit problem
I need help solving this problem without redefining the greatest interger function, is that possible? $$\lim_{x \, \to \,\frac {1}{2}^-}[3x-\frac {1}{2}]$...
Apr 21, 2026 2 VIEWS
What exactly is Laplace transform?
I've been working on Laplace transform for a while. I can carry it out on calculation and it's amazingly helpful. But I don't understand wh...
Apr 21, 2026 1 VIEWS
What is $\lim_{x \rightarrow 0} x^0$?
What is $$\lim_{x \rightarrow 0} x^0$$? Would this equal to $\lim_{x \rightarrow 0}x^x = 1$? If the limit is undefined, would $\lim_{x \rightarrow 0^+} x^...
Apr 21, 2026 1 VIEWS
Solve for x: [2x] = [x] where [.] stands of greatest integer function.
I have solved this question graphically and the result seems to be [$\frac{-1}{2}, \frac{1}{2}$) However I am unable to even think of a process to solve t...
Apr 21, 2026 1 VIEWS