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Vesnalui [34]
2 years ago
11

Which equation is the slope-intercept form of the line that passes through (-3,5) and is parallel to the of y=−2\3x+5

Mathematics
1 answer:
irinina [24]2 years ago
8 0

Answer:

y = -2/3x + 3

Step-by-step explanation:

y = -2/3x + b

5 = -2/3(-3) + b

5 = 2 + b

3 = b

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For what values of x is f(x) = |x + 1| differentiable? I'm struggling my butt off for this course
pav-90 [236]

By definition of absolute value, you have

f(x) = |x+1| = \begin{cases}x+1&\text{if }x+1\ge0 \\ -(x+1)&\text{if }x+1

or more simply,

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.

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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

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Step-by-step explanation:

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Hi,

I assume the forward slash meant it as a fraction VS it being a division symbol. To answer your question, the remainder is 10.

Hope this helps.

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