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16 questions linked to/from Pedagogy: How to cure students of the "law of universal linearity"?
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4 votes
3 answers
183 views

These are some common mistakes high schoolers make: $$ \sqrt{a + b} = \sqrt{a} + \sqrt{b} $$ $$ \log(a+b) = \log (a) + \log(b)$$ So I can obviously show numeric examples to say why these are wrong, ...
meskier's user avatar
  • 41
19 votes
5 answers
63k views

Regard this statement $ x \ge 0$. According to my teacher, by negating this statement, it will become $ x < 0$. Why is this so; why does the $\ge$ morph into $<$, and not into $\le$?
Mack's user avatar
  • 4,727
20 votes
9 answers
4k views

I'm in seventh grade and my teacher wasn't able to explain this to me. Why is $\ \frac{c}{a+b}\neq \frac ca +\frac cb,\,$ but $\ \frac{a+b}c = \frac{a}c + \frac{b}c$? I'm sorry if this is obvious. ...
bluesky777's user avatar
  • 201
10 votes
5 answers
5k views

Say I have $\min(5x_1,x_2)$ and I multiply the whole function by $10$, i.e. $10\min(5x_1,x_2)$. Does that simplify to $\min(50x_1,10x_1)$? In one of my classes I think my professor did this but I'm ...
TheHopefulActuary's user avatar
  • 4,880
2 votes
8 answers
2k views

So I have $\sqrt{a^2+b^2}$. I thought that this was equal to $a^2+b^2$ but it is not. However, even if I convert the square root to powers, I get (based on the power rule $(a^m)^n = a^{mn}$), I get $(...
That Guy's user avatar
  • 1,369
1 vote
5 answers
6k views

Example: Let's presume one was attempting to isolate m below: A common mistake would be: $k^2 = m^2 + n^2 \to k = m +n$ Even though: $k^2 = m^2 + n^2 \to k \neq m +n$ If you apply a square root to ...
MacroGuy's user avatar
  • 81
2 votes
4 answers
2k views

Find $$\lim_{x \to 2} \frac{4-x^2}{3-\sqrt{x^2+5}}$$ (without L'Hopital) Where is the following wrong? (The limit is 6.) \begin{align}\lim_{x \to 2} \frac{4-x^2}{3-\sqrt{x^2+5}}& =\lim_{x \to 2} \...
gbox's user avatar
  • 13.7k
0 votes
8 answers
227 views

I just don't get why this isn't true.
Uchuuko's user avatar
  • 81
3 votes
3 answers
1k views

$$\csc^2+\sec^2=1?$$ I thought I could just use reciprocal from the other formula $\sin^2+\cos^2=1$, can you explain what's wrong?
John's user avatar
  • 49
2 votes
3 answers
309 views

I wanted to calculate the square root of 80, so I did $\sqrt{80} = \sqrt {81-1} = 9-1=8$ I do not know what I did wrong, can someone correct me, as $\sqrt{80}$ is about $8.944$.
math love's user avatar
  • 49
-1 votes
3 answers
755 views

And viceversa It should be tha same, because sqrt(x)+sqrt(x) = sqrt(2x) If not, why?
user3501165's user avatar
  • 39
0 votes
3 answers
318 views

Is $(\sin 48)/2$ the same as $\sin 24$? Does $(\sin 48)/2$ simplify to $\sin 24$? I appreciate the fact the sine graph is curved, so would this mean that you could not simply divide the $48$ on the ...
Toby Cannon's user avatar
  • 147
1 vote
2 answers
116 views

$$\lim_{n \to \infty}a_n=\dfrac{5^{3\cdot n}}{2^{\left(n+1\right)^2}}$$ I am trying to solve it using the squeeze theorem. I have opened the expression to $$a_n=\dfrac{5^3\cdot 5^n}{2^{n^2}\cdot2^{2n}...
gbox's user avatar
  • 13.7k
0 votes
1 answer
364 views

I'm really confused with working with sequences of functions and their sup. Let A be a non-empty subset of $\mathbb{R}$. For all $n \in \mathbb{N}$ and let $f_n : A \to\mathbb{R}$ be a continuous ...
Analysis is fun's user avatar
  • 75
1 vote
2 answers
217 views

There is something I am misunderstanding about simplification. For example: Given: $y^6$$z^6$/$x^6$ Why can I not take the 6th roof of both to simplify to $yz$/$x$? I clearly see that both ...
Sphygmomanometer's user avatar
  • 295

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