On $[-2,2]$: $\max(|x|,x^2)=x^2$ when $x^2\ge|x|$, i.e., $|x|\ge1$; equals $|x|$ when $|x|\le1$.

So $f(x)=|x|$ for $|x|\le1$ and $f(x)=x^2$ for $1\le|x|\le2$.

Check non-differentiability: At $x=0$: $|x|$ is not differentiable. At $x=\pm1$: left-hand $f'=\pm1$, right-hand $f'=2x=\pm2$ — not equal, so not differentiable. At $x=\pm2$: $f(2^-)=4$, $f(2^+)=4$; $f'(2^-)=4$, $f'(2^+)=-2$ — not differentiable.

So $S=\{-2,-1,0,1,2\}$.

Note that $10{,}000{,}000 = 10^7$.

Comparing $9^7$ vs $10^7$: since the base $9 < 10$ and both exponents are equal and positive, we have $9^7 < 10^7$.

Therefore Column B ($10^7$) is greater than Column A ($9^7$).

Power: watt (J/s). Energy: joule; Force: newton; Velocity: m/s.

Comparing the business's records with the supplier's statement is the most effective way to find missing credit notes, as the supplier will have recorded the credit note even if the business forgot to. A trial balance or control account only checks internal consistency.

The expression $\dfrac{x}{|x|}$ is the sign function of $x$:

• If $x > 0$: $\dfrac{x}{|x|} = \dfrac{x}{x} = 1$ → equal to Column B
• If $x < 0$: $\dfrac{x}{|x|} = \dfrac{x}{-x} = -1$ → less than Column B

Since $x$ can be positive or negative, and we get different results, the relationship cannot be determined from the information given.