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2 years ago

Please help me work this out ASAP with a method preferably??!!

Mathematics

1 answer:

avanturin [10]2 years ago

7 0

$\huge{ANSWER}$

$\frac{ {11}^{13} \times {11}^{3} }{ {11}^{7} }$

As we know if powers are there is multiplication with same base gets added and with division gets substracted.

$\frac{{11}^{13 + 3}}{ {11}^{7}}$

${11}^{16 - 7}$

${11}^{9}$

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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.

For x > -1, we have

(x + 1)' = 1

while for x < -1,

(-x - 1)' = -1

More concisely,

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

Note the strict inequalities in the definition of f '(x).

In order for f(x) to be differentiable at x = -1, the derivative f '(x) must be continuous at x = -1. But this is not the case, because the limits from either side of x = -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 f(x) is differentiable everywhere on its domain, except at the point x = -1.

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2 years ago

{[20/(8+2)]^6+6}/(4^2/2)

Naddika [18.5K]

So for this problem we need to do order of operations so the very first step that we need to do here is (8+2) because that is the smallest enclosed symbols (8+2)=10 next divide by 20 because that is the next step in the equation which 20/10=2, so now we have {[2]^6+6} and due to order of operations the next step here is to take 2 to the power of 6 which is 64 so now we have {64+6} which is 70 so now we have 70/(4^2/2) and due to order of operations we do the parentheses first and that would mean that we do 4^2 because exponents come after parantheses like so,
70/(16/2) now we do 16/2 because its still inside the paranthesess so 16/2=8 so now we have 70/8 and that equals are end answer of 8.75 Enjoy!=)

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