Answers
f ' (0) exists if the limit,
[tex]\displaystyle \lim_{h\to0}\frac{f(0+h)-f(0)}h[/tex]
exists, and f ' (0) has the value of this limit.
In order for this limit to exist, both limits from either side of h = 0 must exist.
Suppose h < 0. Then 0 + h is also negative, so by definition of f(x) we have
f (0 + h) = ((0 + h) + 1)² = h ² + 2h + 1
Then in the limit, if h is approaching 0, it must be from below or from the left:
[tex]\displaystyle \lim_{h\to0^-}\frac{f(0+h)-f(0)}{h} = \lim_{h\to0^-}\frac{(h^2+2h+1)-1}{h} = \lim_{h\to0^-}(h+2) = 2[/tex]
Now suppose h > 0, so that 0 + h is positive and h approaches 0 from above or from the right. Then
f (0 + h) = 2 (0 + h) + 1 = 2h + 1
and
[tex]\displaystyle \lim_{h\to0^+}\frac{f(0+h)-f(0)}h = \lim_{h\to0^+}\frac{(2h+1)-1}{h} = \lim_{h\to0^+}2 = 2[/tex]
Both one-sided limits match, so f ' (0) = 2.
Related Questions
PLEASE ANSWER QUICK!
Simplify the expression 7(2g+7)-4
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PLEASE HELPPP
Richard divided a 1.954-L bottle of spicy tomato juice
equally among 5 glasses. How much juice is in each glass?
Answers
Answer:
390.8ml
Step-by-step explanation:
1.954 divided by 5=0.3908 litres
0.3908liters=390.8ml
HELPPPPPP PLZZZ, find the height of the figure below with the given volume.
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Ok Now can anybody help due in 1 and a half min will give the brainiest.
Answers
Answer:
-25, 5
Step-by-step explanation:
-22 + -25 = -47
-25/5 minutes = -5
since there is no -5 in speed, then the answer is 5
How many zeros are in the product 4 x 10 7th power
Answers
Answer:
7 or 40,000,000
Step-by-step explanation:
The exponent (^7) is how many zeros for the 10. if there is 10^2 its just 100 because it's 10 * 10 or 100 (notice the zeros in the 10 * 10 equation? yup, there's 2) and the 4 is basically 4 * 10, it changes the 10 like 4*1 but with a lot of zeros if there were exponents (10^2) so just put them together and you get 4 * 10^7
10^7 (its just 10 times itself 7 times) = 10,000,000
4 * 10,000,000 = 40,000,000
Hope this helps
~R3V0
match each term with its definition,
Answers
Answer:
Population-1
Sample- 2
Simulation-4
biased sample- 3
Hurry ASAP) Graph the system of equations. f ( x) = x^2 - 5x + 7 and g(x)=2x + 1. Which statements are true about the solutions to the system of equations? Select each correct answer. ( I accidentally clicked on option A but I don't know the answer at all). Will Mark Brainliest.
Answers
Answer:
N/A
Step-by-step explanation:
Get the Desmos graphing calculator app. it is very helpful when graphing and needing to be able to compare functions
What does APS Stand for
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apple presents stop motion studios?
different time and place
Hey circle is divided into 24 sectors are shown below the sectors were rearranged into the figure shown below by placing the sector side-by-side this figure can be used to derive the equation for the area of a circle which statement about the figure is true
Answers
Answer:
the answer is two
Step-by-step explanation:
The equation is
The figure is similar to a parallelogram , with a base length equivalent to the circumference of the circle and a height equivalent to the radius of the circle
What is a Circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle
Given data ,
Let the radius of the circle be represented as r
Now , the equation will be
The circumference of the circle C = 2πr
And , the circle is divided into 24 sectors and it is placed side-by-side
The figure formed is in the shape of a parallelogram
The base length of the parallelogram = circumference of the circle
And ,
Height of the parallelogram = radius of the circle r
Hence , the base length is the circumference and height is the radius of the circle
To learn more about circle click :
https://brainly.com/question/28391204
#SPJ2
Start with x2 - 6x + 8 = 0 and complete the square, what is the equivalent equation?
es -))
A)
(x + 3)2 = 1
B)
(x+3)2 = 9
C)
(x - 3)2 = 1
D)
(x-3)=9
Answers
Which figures can have all of the properties shown below
Answers
Answer:
quatrolatiral, square, rectangle
pls help me giving brainless.
Answers
Answer: about 8 dollars
Step-by-step explanation:
2*12=24
8*12=96
12*12=144
Answer:
8 dollars
Step-by-step explanation:
the math comes out to 6.5 dollars per person and 8 is the closest
no links help me
Parents are raising money for new playground equipment. They need $682.56 to purchase swings and receive a $200.00 donation. The remaining amount will be equally divided among 8 different student groups to raise. How much money will each student group need to raise in order to purchase the swings? Your answer should start with the $ and should only include numbers and a decimal point. *
Answers
Answer:
$53.57
Step-by-step explanation:
First, you have to subtract 200 from 628.56 to get 428.46
Then, you do 428.46/2 = 53.57, which is your answer
Hope this helps!
Step-by-step explanation: $682.56 - 200 of the donations = 482.56
help with math thanks so much:)
Answers
Answer:
4/3Step-by-step explanation:
1/2 ÷ 2/3 = 1/2 x 3/2 = 3/4 -_- so easy
Answer:
The first one is three the second is four
Step-by-step explanation:
1/2÷2/3 (do copy, dot, flop)
1/2·3/2
1·3=3
2·2=4
3/4
The two numbers in bold are the answers
Evaluate the algebraic expression 3f + g,when f = 6, g = 8, h = 12 and j = 2
Answers
I think 26 is the answer
look at pic 10 pts will mark brainilest
Answers
Answer:
There is nothing attached
Step-by-step explanation:
Where is the picture?
k over 1.5 equals 3 what is k
Answers
Answer:k=4.5
Step-by-step explanation:4.5/1.5=3
Solve the quadratic equation by factoring.
6x 2 + 24x = 0
Answers
Answer:
x=0
2(3x+12x)
FACTORED ANSWER
2(15)x)
Step-by-step explanation:
Answer:
[tex]x = 0[/tex]
Step-by-step explanation:
Factor 6x⋅2 out of 6x⋅2+24x.
[tex]6x \times (2(1 + 2)) = 0[/tex]
Multiply 2 by 6.
[tex]12x(1 + 2) = 0[/tex]
Add 1 and 2.
[tex]12x \times 3 = 0[/tex]
multiply 3 by 12.
[tex]36x = 0[/tex]
Divide each term by 36 and simplify.
[tex]x = 0[/tex]
therefor, the answer is 0.
What's the circumference of a
circle with a diameter of 18 inches?
Use 3.14 for n.
C = [?] inches
Answers
Answer:
56.55 inches
Step-by-step explanation:
10 POINTS!!!!which polynomial represents the sum below ?
Answers
Answer:
b
Step-by-step explanation:
use calculator next time
B. 3x³ + 8x² + 9x + 12 is the answer.
hope it helps..
Match the values with the statistical measures for these data points.
20, 20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26
Answers
Answer:
20, 20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26
Step-by-step explanation:
median (middle number) is (23 + 24) / 2 = 47/2 = 23.5 <== median
Q1 = (21 + 22) / 2 = 43/2 = 21.5 <== lower quartile
Q3 = (25 + 25) / 2 = 50/2 = 25 <== upper quartile
Your welcome! (Please correct me if im wrong!)
Please mark brainiest
GIVING OUT BRAINLIEST TO WHOEVER CAN PROVIDE THE CORRECT ANSWER !! Asap
Answers
Joseph is planning to meet up with his friend Naomi. Joseph jogs from his house traveling at a rate of 4
miles per hour. Naomi is initially 27 miles from Joseph's house and travels towards Joseph at 5 miles per
hour.
a) Show your solution graphically.
b) How many hours went by before they met?
hours
c) How many miles were they from Joseph's house when they met?
miles
30
25
Joseph
Answers
Answer:
It took 3 hours for the two to meet, and they were 12 miles from Joseph's home when they met.
Step-by-step explanation:
Since Joseph is planning to meet up with his friend Naomi, and Joseph jogs from his house traveling at a rate of 4 miles per hour, while Naomi is initially 27 miles from Joseph's house and travels towards Joseph at 5 miles per hour, for To determine how many hours went by before they met and how many miles were they from Joseph's house when they met, the following calculations should be performed:
27 - (4 + 5) = 27 - 9 = 18
27 - (4 + 5) x 3 = 0
Therefore, it took 3 hours for the two to meet.
4 x 3 = 12
Thus, they were 12 miles from Joseph's home when they met.
What are the coordinates of point (-2, -4) after a 180 degree rotation?
Answers
Answer:
(2, 4)
Step-by-step explanation:
Anytime you rotate a point 180° about the origin, the x-coordinate and y-coordinate become their opposites.
(x,y) becomes (-x,-y)
Emily jogged 8 miles due north, then turned east and jogged 15 miles. How many miles is
she from her starting point?
Answers
Answer:
The answer is 120
Step-by-step explanation:
I got it by timing 8 and 15 , and I got 120
ANSWER THE QUESTION FOR BRAINLIEST
Answers
Answer:
C, the graph is increasing when x is between -1 and 2.
Step-by-step explanation:
When it is increasing, it is getting higher up the y axis. The other two lines are going lower down the x axis so they are decreasing. This means that it has to be C.
hope this helps :)
find the value of x in the Triangle shown below x=?
Answers
Answer:
x = 66°
Step-by-step explanation:
unmarked angle = x because it is an isosceles triangle.
The sum of all three interior angles of any triangle = 180°
So:
2x + 58° = 180°
2x = 122°
x = 66°
HELP PLEASE!!!!!!!!!!!
Answers
Answer:
x = 4
Step-by-step explanation:
7.5 + 7.5 = 15
[tex]\frac{x}{8}[/tex] = [tex]\frac{7.5}{15}[/tex]
cross multiply
15x = 60
divide
x = 4
or
since the bigger one is 2x smaller
8/2 = 4
Please help me wiht this
Answers
Answer:
Kevin
Step-by-step explanation:
Math\Angles
Find the missing angle
Answers
Answer:
x = 180° - 72° = 108°
Because x and 72 degrees are supplementary angles.
Look at the attached screenshot for my answer!!! Hope this helps!! Have a wonderful life now!!!