By definition of absolute value, you have
or more simply,
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,
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:
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.
Answer:
Hope this helps! Brainliest please
Step-by-step explanation:
1. Divide both by 5, so the correct answer would be 5/9, and then multiply both by 3, so the correct answer would be 75/135. The answer is 5/9,75/135
2. 4 and 2/7 because 7 *4=28. That leaves 2 sevenths over.
3. Divide both by 9. Your answer is 3/4
Answer: the service charge per hour for premium services is $5.5
the service charge per hour for regular services is $3
Step-by-step explanation:
Let x represent the service charge per hour for premium services.
Let y represent the service charge per hour for regular services.
One customer was charged $38 after spending 2 h in premium areas and 9 regular hours. It means that
2x + 9y = 38- - - - - - - - - - - 1
Another customer spent 3 h in premium areas and 6 regular hours and was charged $34.50. It means that
3x + 6y = 34.5- - - - - - - - - - -2
We would eliminate x by multiplying equation 1 by 3 and equation 2 by 2. It becomes
6x + 27y = 114
6x + 12y = 69
Subtracting, it becomes
15y = 45
y = 45/15
y = 3
Substituting y = 3 into equation 1, it becomes
2x + 9 × 3 = 38
2x + 27 = 38
2x = 38 - 27 = 11
x = 11/2 = 5.5
Pretty sure it’s the second option because length would be 3w+2
and width would be w+1 and with area you have to multiply so it would just be the (w+1)(3w+2)
The factorization of the numbers is obtained as
(a) 36 = 2² x 3²,
(b) 60 = 2² x 3 x 5,
(c) 84 = 2² x 3 x 7,
(d) 99 = 3² x 11 and
(d) 180 = 2² x 3² x 5
<h3>Factor of the numbers</h3>
To factorize the numbers we use their factors as show below;
<h3>Factors of 36</h3>
36 = 2² x 3²
<h3>Factors of 60</h3>
60 = 2² x 3 x 5
<h3>Factors of 84</h3>
84 = 2² x 3 x 7
<h3>Factors of 99</h3>
99 = 3² x 11
<h3>Factors of 180</h3>
180 = 2² x 3² x 5
Thus, the factorization of the numbers is obtained as 36 = 2² x 3², 60 = 2² x 3 x 5, 84 = 2² x 3 x 7, 99 = 3² x 11 and 180 = 2² x 3² x 5.
Learn more about factorization here: brainly.com/question/25829061
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