The absolute value function is defined as
[tex]|x| = \begin{cases}x & \text{for }x \ge 0 \\ -x & \text{for }x < 0\end{cases}[/tex]
If x is strictly positive (x > 0), then |x| = x, and d|x|/dx = dx/dx = 1.
If x is strictly negative (x < 0), then |x| = -x, and d|x|/dx = d(-x)/dx = -1.
But if x = 0, the derivative doesn't exist!
In order for the derivative of a function f(x) to exist at x = c, the limit
[tex]\displaystyle \lim_{x\to c}\frac{f(x) - f(c)}{x-c}[/tex]
must exist. This limit does not exist for f(x) = |x| and c = 0 because the value of the limit depends on which way x approaches 0.
If x approaches 0 from below (so x < 0), we have
[tex]\displaystyle \lim_{x\to 0^-}\frac{|x|}x = \lim_{x\to0^-}-\frac xx = -1[/tex]
whereas if x approaches 0 from above (so x > 0), we have
[tex]\displaystyle \lim_{x\to 0^+}\frac{|x|}x = \lim_{x\to0^+}\frac xx = 1[/tex]
But 1 ≠ -1, so the limit and hence derivative doesn't exist at x = 0.
Putting everything together, you can define the derivative of |x| as
[tex]\dfrac{d|x|}{dx} = \begin{cases}1 & \text{for } x > 0 \\ \text{unde fined} & \text{for }x = 0 \\ -1 & \text{for }x < 0 \end{cases}[/tex]
What is the median of 8,19,36,46,56
Answer:
median = 36
Step-by-step explanation:
The median is the middle value of the data arranged in ascending order.
8 19 36 46 56
↑ middle value
median = 36
6=2(y+2) solve for what is y?
Answer:
y is 1
Step-by-step explanation:
Answer:
y = 1
Step-by-step explanation:
First divide both sides by 2
this gives you 3 = y+2
then subtract 2 from each side giving you y = 1
Billy and Michael have 2 lemonade stands. Billy charges $2 per lemonade plus a flat rate of $2.
Michael charges $3 per lemonade plus a flat rate of $1.
How many lemonades would they have to sell to be making the same amount of money?
Which expression shows the number 19.65 correctly decomposed?
19 + 0.6 + 0.05
10 + 9 + 0.6 + 0.05
10 + 0.6 + 0.05
19 + 9 + 0.6 + 0.05
Answer: 10 + 9 + 0.6 + 0.05
Answer:
..............................................................
Step-by-step explanation:
..........................................................................
..........................................................................
What's the circumference of a
circle with a radius of 5 inches?
Use 3.14 for i.
C = [?] inches
Answer:
31.4 inches
Step-by-step explanation:
c = 2 * 3.14 * r
c = 2 * 3.14 * 5
C = 31.4 inches
Jacob followed a recipe that requires 2 cups of water for ever 3 cups of flour. If he
used 8 cups of flour, how many cups of water did he use?
2 2/3
4
5 1/3
12
Thank u SOOOOOOOOOO much if u helped me
Answer:
he used 5 1/3 everything else is to low or high
What is
2(3x + 4) = -28
Answer:
x= 10/3
or
x= 3.334
Depending on simplified form asked.
Step-by-step explanation:
6x +8 =28
subtract 8 from both sides
6x = 20
divide by 6
x=20 /6
x= 10/3 or x =3.334
if you like my answer, please mark me brainliest !! thanks !! <3
Select the choice that translates the following verbal phrase correctly to algebra: (1 point)
the product of 12 and y increased by 11
12(y + 11)
12y + 11
12 + 11y
12(11y)
Answer:
[tex]⟼12(y + 11)[/tex]
How to simplify -7 + 3 - 20
Answer:
-24
Step-by-step explanation:
-7 +3 is -4
-4+-20 is -24
-7 + 3 - 20
= -4 - 20
= -4 + -20
= -24
______
Hope it helps ⚜
Andre road his bike at a constant speed he rode one mile in 5 minutes which of these equations represent the amount of time t (in minutes) that it takes him to ride a distance of d miles?
a:t=5d
b:t=1/5d
c=d+4
dt=d-4
Answer: Hello!
Time taken to drive 1 mile = 5 minutes. Now we have to find the amount of time t (in minutes) taken by him to right distance d so we can again use same formula. Since the answer will be equation A. t=5d.
A. t=5d
Step-by-step explanation:
Mark me brainest please. Hope I helped! Hope you make an 100% Anna♥
i am stuck on this zearn lesson someone pls help
Answer:
2 or 2/1
Step-by-step explanation:
For every cup of water there is 1 cup of water. As seen in the ration 6:12 (reduced to 1:2) and 1/2:1 (increased to the whole number of 1:2)
What is the missing value?
X
1
2
3
4.
5
у
6
11
16
21
Answer:
25555555557777385381938$88388+2
Write an equation in slope-intercept form for the line passing through the two points (0,-2) and (3,0)
Answer:
y = (2/3)x - 2
Step-by-step explanation:
This problem is interesting in that both the x- and the y-intercepts are given. The y-intercept is (0, -2), and so 'b' in 'y = mx + b' must be -2:
y = mx - 2. The x-intercept is (3, 0), so we know that y = 0 when x = 3:
0 = m(3) - 2
This latter result must be solved for m: 3m = 2, or m = 2/3.
Then the desired equation is y = (2/3)x - 2.
i need help!!!!!!!!!!
Answer: Read the Explanation
Step-by-step explanation:
m<7 = 120
m<5 = 120
m<6 = 60
m<2 = 60
The reason why they are 60 is because they are supplementary angles to complete a straight line so like since 3 = 120 4 = 60 since its a straight line.
Answer:
ly
Step-by-step explanation:
A grocery store buys cashews for
$8 per pound. The store wants to
markup the price by 20%. Which
expression below could be used to
find the new price of the cashews
Answer:
9.6
Step-by-step explanation:
20%of 8=8*20/100 =1.6 and the new price of the cashews is1. 6+8=9.6
- You find a recipe for cookies. You want
to know how much sugar is in each cookie.
The recipe uses 3/4 cup of sugar and makes
one-dozen cookies. Find the amount of sugar
per cookie. Show unit rate work. Use fractions
not decimals.
Answer:
1/16
Step-by-step explanation:
3/4 ÷ 12
3/4 x 1/12
3/48 or 1/16
Hope this helps!
Answer:
1/16
Step-by-step explanation:
recipe uses 3/4 cup of sugar for one dozen cookies
3/4 cup ------ 12 cookies
x ------- 1 cookie
x * 12 = 3/4
x = 3/4 / 12
x = 3 / (4*12)
x = 1 / 4*4
x = 1/16
answer..............................
Answer:
yes
Step-by-step explanation:
The population of a place was 56000. Next 5 years it is expected to rise by 50%. What will be the population in next 5 years?
Answer:
84000 people
Step-by-step explanation:
So next 5 year wil be 56000 + 50%
56000 = 100%
50% = 56000 / 2
50% = 28000
56000 + 28000 = 84000
Anyone helps me pleaseeeeee✨
I will so so so love you if you help me to solve it!!!!!!!!!
Answer: Hope it helps :)
Step-by-step explanation:
The essential thing to learn from this lesson is the translation of equations. When f(x) = f'(x) + a, the graph of the equation is shifted up by a units.
When f(x) = f'(x + a), the graph of the equation is shifted left by a units.
3x + 3 = 2x + 12 i need help for this answer
Answer:
X=9
Step-by-step explanation:
3x+3=2x+12
3x-2x=12-3
x=9
HELP AGAIN PLSSSSSSS
Answer:
didn't you already do it? im confused
Step-by-step explanation:
Creflo is 6 years older than Dean.
Raheem is twice as old as Creflo.
The sum of their ages is 34.
Work out the ratio of Dean's age to Creflo's age to Raheem's age.
solve pls brainliest
Answer:
B) y = kx
Step-by-step explanation:
A Proportional relationship should have an equivalent ratio
All of the answers have a pass through the origin except y = kx because k is unknown.
Please show all work
No links please
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today! I hope you are having a nice day.
So we can solve this in one single step, I'll start off with solving it.
So first we know that [tex]AB=DF[/tex] and of which [tex]DF[/tex] is the Hypotenuse of triangle [tex]DE F[/tex].
Since the hypotenuse is equal to one of the legs of the 2nd triangle, we cannot use any rule that has Side in it as they are both not really getting us anywhere.
We do know that [tex]<ABC=<DE F[/tex] as they are both 90 degrees.
As we don't have enough proof, these triangles are not congruent as we would need to do/prove rule RHS.
Cheers!
Melanie buys a carrying case for her new laptop, which costs 125% as much as her old laptop case. The price of her new laptop carrying case is $65. If n represents the cost of her old laptop carrying case, which proportion can be used to find n?
Answer:
C
Step-by-step explanation:
Because don't know old laptop cost.
So 65 dollars represent 100% and n(old case) represents 125%.
Confused help please
Answer:
130
Step-by-step explanation:
1 and 2 form a straight line, so they are supplementary. That means they add up to 180. So,
a1+a2=180
50+a2=180
a2=130
Answer:
it would be B.130
Step-by-step explanation:
considering an angle can only go to 180* subtract 50 from 180 and you get 130
can someone please assist me in these equations!?!?! pls
Answer:
1. -9 because -9x6= -54, -10 because 5 x -10= -50, and x=1 because -2 x 1= -2
Step-by-step explanation:
Answer:
1. = −9
2. = −10
3. = 1
Step-by-step explanation:
How do you know it is positive or negative in exponents.
Find slope of line (I need to see if you get the same answer as me to know if it’s right)
Answer: -5
Step-by-step explanation:
Point #1: (-4, 2)
Point #2: (-3, -3)
Slope: -5
Answer:
Slope=M=-5Full equation y=5/7x-18Step-by-step explanation:
(-3,-3),(4,2) y=mx+b
input variables for the full equation for slope, rise/run
it rise's up 5 and runs back -1 so slope is -5
CAN SOMEONE HELP ME PLEASE ASAP!
quick question is this area or perimeter?
Answer:
2 and 3
Step-by-step explanation:
to be similar, there must have been the same scaling factor applied for length and width.
when going from 2 to 3 the width changes from 5 to 7, that is a changing factor of 7/5 = 1.4
and the length changes by the same factor :
6.5 × 7/5 = 1.3 × 7 = 9.1