How can we efficiently find square root of 5 in a mod prime field. By quadratic reciprocity we can argue that 5 is a square in modulo p(prime) is p is squ...

Let $f\in C^2[a,b]$. The composite trapezoidal rule is given by $$T_n[f]:=h\left(\frac{f(a)+f(b)}{2}+\sum_{k=1}^{n-1}f(x_k)\right)\;\;\;\;\;\left(h:=\frac...

In the image below, why is the given sum equal to +10, 627 ? Why the 10's complement of +9286 is 990714 and not 000714 (10000-9286) ? Why was there a...

I ran into a question on a practice test which said "What is the difference between -8 and -3? I am 13, and I am quite capable of subtracting negative num...

Earlier in algebra, we spent over 20 minutes trying to figure out $$ \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{R_e} \,\,\,\, \text{solve for }R_2 $$ when t...

In looking at the definition of vertical tangent lines in some popular calculus texts, I noticed that there are a few different definitions for this term,...

I can find the equation of a line using the slope-intercept form if I have two points on the line. However I was trying to do the same with the standard f...

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves $y=x^2$, $y=0$, $x=1$, and $x=2...

I have to prove the condensation test of Cauchy by tomorrow and I am really unconfident about what I did: $$\sum_{n=1}^\infty a_n\text{ converges } \iff \...

$$\sigma = \begin{bmatrix} 1 &2 &3 &4 &5 &6 &7 &8 &9 \\ 1&5 &7 &4 &6 &9 &3 &2 &8 \end{bmat...