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oee [108]
3 years ago
13

A store donated cases of crayons to a daycare center. Each case holds 24 boxes of crayons; each box holds 8 crayons. How many cr

ayons did the center receive?
Mathematics
2 answers:
Sedbober [7]3 years ago
8 0

Answer:

Step-by-step explanation:

24x8 =192 crayons

Diano4ka-milaya [45]3 years ago
8 0

Answer:

192

Step-by-step explanation:

For each case that was donated, it will hold 192 crayons. I got this by multiplying 24×8.

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By definition of absolute value, you have

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f(x) = \begin{cases}x+1&\text{if }x\ge-1\\-x-1&\text{if }x

On their own, each piece is differentiable over their respective domains, except at the point where they split off.

For <em>x</em> > -1, we have

(<em>x</em> + 1)<em>'</em> = 1

while for <em>x</em> < -1,

(-<em>x</em> - 1)<em>'</em> = -1

More concisely,

f'(x) = \begin{cases}1&\text{if }x>-1\\-1&\text{if }x

Note the strict inequalities in the definition of <em>f '(x)</em>.

In order for <em>f(x)</em> to be differentiable at <em>x</em> = -1, the derivative <em>f '(x)</em> must be continuous at <em>x</em> = -1. But this is not the case, because the limits from either side of <em>x</em> = -1 for the derivative do not match:

\displaystyle \lim_{x\to-1^-}f'(x) = \lim_{x\to-1}(-1) = -1

\displaystyle \lim_{x\to-1^+}f'(x) = \lim_{x\to-1}1 = 1

All this to say that <em>f(x)</em> is differentiable everywhere on its domain, <em>except</em> at the point <em>x</em> = -1.

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