!!!!! determine the function being differentiated, and the number at which its derivative is being evaluated. Where possible, evaluate the limits using differentiation.
Answers
Recall that the derivative of a function f(x) at a point x = c is given by
[tex]\displaystyle f'(c) = \lim_{x\to c} \frac{f(x) - f(c)}{x - c}[/tex]
By substituting h = x - c, we have the equivalent expression
[tex]\displaystyle f'(c) = \lim_{h\to0} \frac{f(c+h) - f(c)}h[/tex]
since if x approaches c, then h = x - c approaches c - c = 0.
The two given limits strongly resemble what we have here, so it's just a matter of identifying the f(x) and c.
For the first limit,
[tex]\displaystyle \lim_{h\to0} \frac{\sin\left(\frac\pi3 + h\right) - \frac{\sqrt3}2}h[/tex]
recall that sin(π/3) = √3/2. Then c = π/3 and f(x) = sin(x), and the limit is equal to the derivative of sin(x) at x = π/3. We have
[tex](\sin(x))' = \cos(x)[/tex]
and cos(π/3) = 1/2.
For the second limit,
[tex]\displaystyle \lim_{a\to0} \frac{e^{2a} - 1}a[/tex]
we observe that e²ˣ = 1 if x = 0. So this limit is the derivative of e²ˣ at x = 0. We have
[tex]\left(e^{2x}\right)' = e^{2x} (2x)' = 2e^{2x}[/tex]
and 2e⁰ = 2.
Related Questions
only help if u know :D
Answers
The number of students in the school given the number of people that attended the dance is 128.
How many students are there?Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.
Number of students = number of students at the dance / percentage that attended the dance
32 / 25%
32 / 0.25 = 128
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(2) If the price of an item is represented by p, a final price of 0.7p indicates a discount of what percent?
Answers
Answer:
30%
Step-by-step explanation:
First subtract: 1 - .70 = .30
Then move decimal over to the right 2 times and add percentage sign instead of the decimal: 30%
Question Progress
10
Find the value of:
a) x² when x = 6
Answers
Answer:
x^2= 36
Step-by-step explanation:
since x = 6
therefore, x^2 = 6×6=36
2x=-4(1/4-3/4 x)+4
solve for x
Answers
Answer:
x=-3
Step-by-step explanation:
isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
Step-by-step explanation:
Multiply part of the right side by - 4
2x = -4*1/4 + 4* 3x/4 + 4 Combine
2x = - 1 + 3x + 4 Combine again
2x = 3 + 3x Subtract 3x both sides
2x - 3x = 3 Combine
-x = 3 Multiply by -1.
-1 * -x = - 1 * 3
x = - 3
Find the measures of the angles of an isosceles triangle where the ratio of the vertex angle to one of the base angles is 1:2.
Answers
Answer:
Angles of the isosceles triangle are 36°, 72° , 72°
Step-by-step explanation:
Vertex angle : Base angle = 1 : 2
Vertex angle = x
Base angle = 2x
Sum of all angles of a triangle = 180°
x + 2x + 2x = 180°
5x = 180
x = 180 ÷ 5
x = 36°
2x = 2 *36 = 72°
Angles of the isosceles triangle are 36°, 72° , 72°
Please Help I Don't Undertand.
Answers
If triangles AMN and ABC are similar, then
AM/AB = AN/AC
or
AM/(AM + MB) = AN/(AN + NC)
Check if this is true:
AM/AB = 21/(21 + 9) = 21/30 = 7/10
AN/AC = 14/(14 + 6) = 14/20 = 7/10
The angle at vertex A is common to both of the triangles.
Then by the side-angle-side (SAS) similarity theorem, the triangles are indeed similar.
Please I need help asap
Answers
Answer:
Option D - x = 3 3/5
Step-by-step explanation:
Lets make the left side into an improper fraction :
2 2/5 = 12/5
Now let's make both fraction into equivalent ones but with the same denominator :
2/3 = 10/15
12/5 = 36/15
Now we substitute the equivalent values back into the equation :
10/15 × x = 36/15
Now we multiply both sides by 15 to remove the denominators:
10 × x = 36
Now we divide both sides by 10 and simplify :
x = 36/10
x = 18/5
x = 3 3/5
So our answer will be Option D
Hope this helped and brainliest please
What is the (LCM) of 5/6 and2/5
Answers
Answer:
30
Step-by-step explanation:
[tex]\frac{5\cdot\frac{6}{6} }{2\cdot\frac{6}{6} } = \frac{25}{30}, \frac{12}{30}[/tex]
Using graphing, what is the approximate solution of this equation? 3xˆ2-6x-4 = -2/x+3 + 1 A. x = .64
B. x = .33
C. x = .18
D. x = 2.60
Answers
Answer: c
Step-by-step explanation:
The required values on the graph, the solution is approximate x = -0.33.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
To solve this equation, we can begin by combining like terms on the left-hand side:
3x² - 6x - 4 - 2/x + 3 + 1 = 0
3x² - 6x - 2/x = -3
Next, we can factor out the x term:
x(3x - 2) - 2(3x - 2) = -3
(x - 2)(3x - 2) = -3
Since the equation is equal to -3, we can add 3 to both sides to get:
(x - 2)(3x - 2) + 3 = 0
We can then factor the left-hand side to get:
(x - 2)(3x - 2 + 3) = 0
(x - 2)(3x - 2 + 3) = (x - 2)(3x + 1) = 0
This equation has two solutions: x = 2 and x = -1/3.
Approximating these values on the graph, we see that the solution is approximate x = -0.33.
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Factor the algebraic expression.
18a+15
Answers
Answer: 3(6a+5)
We can confirm this by distributing the 3 back in
3*6a = 18a
3*5 = 15
So 3(6a+5) = 3*6a+3*5 = 18a+15
The process of factoring polynomials like this is basically using the distributive property in reverse.
Answer:
3(6a + 5)
Step-by-step explanation:
1) Find the Greatest Common Factor (GCF).
1 - What is the largest number that divides evenly into 18a and 15?
It is 3.
2 - What is the highest degree of a that divides evenly into 18a and 15.
It is 1, since a s not in every term.
3 - Multiplying the results above,
The GCF is 3.
2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
3 (18a/3 + 15/3)
3) Simplify each term in parentheses.
3(6a + 5)
what is the equation of a circle with center (2,4) and radius 7
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Answer:
try texting new food
Step-by-step explanation:
I do not know
PLEASE HELP ME PICTURE BELOW!!!
Answers
Answer:
corographicia
Step-by-step explanation:
its the right answer
Can you help me with this? it would help!
Answers
according to the graph,what is the value of the RANGE when the DOMAIN is 0
Answers
Answer:
it would be nice with a photo dude
Describe the effect the change in scale has on what the graph suggests. a. On graph B, the group of birds seems to have twice as much as the group of mammals. b. The differences between the groups seems much less in Graph A. c. The differences between the groups seems much less in Graph B. d. On graph A, the group of mammals seems to have one-quarter as much as the group of fish. Please select the best answer from the choices provided
Answers
The effect that the change in scale has on what the graph suggests is C. The differences between the groups seems much less in Graph B.
What is a graph?It should be noted that graph simply means a diagram that's used to show the information about a data given.
Here, the effect that the change in scale has on what the graph suggests is that the differences between the groups seems much less in Graph B.
Therefore, the correct option is C.
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simplify the numerical expression- cant write it out so i'm using a pic
Answers
Answer:
-38
Step-by-step explanation:
4-(3^4-6^2)+2(3)÷2
=> 4 - (81-36) + 2(3) ÷ 2
=> 4 - 45 + 2(3)÷2
=> 4 - 45 + 6÷2
=> 4 - 45 + 3
=> -41 + 3
=> - 38
hope this helps :)
Which answer choice has the set of numbers
ordered correctly from least to greatest?
16
13, √, 1.71, 9
3
√. 12, 16, 1.71
4
3
16
1.71, 12, 1
9
O
16.1.71,√, 12
3
9
Answers
Answer:
0
3
3
3
8
9
12,161.71√
I think his is the best order
There are 6 girls and 5 boys in a debate class. The teacher chooses two students at random to lead a class discussion. What is the probability of selecting a girl and then a boy
Answers
Answer:
Step-by-step explanation:
There are 11 students in total.
6 girls.
and 5 boys.
so the probability of selecting a girl is 1/5 because 5 boys or it could be 1/11 if i am not mistaken.
(which i might be)
If k is an integer, which of the
following must be odd?
F. 7k-1
G. 3k + 2
H. 1-5k
J. 7+2k
Answers
Answer:
J
Step-by-step explanation:
F is wrong, Lets say K is 1, then 7-1 = 6
G is wrong, say K is 2, then 6+2 = 8
H is wrong, say K is 1, then 1 - 5 = -4
J is right, Say K is 1, then 7+2 = 9, say K is 2, then 7+4 = 11, any integer used is an odd number
-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)
A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given.
a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.
Please show work!
Answers
Answer:
part 1) BC is 17491 ft
part 2) CD is 6499 ft
Step-by-step explanation:
A jar of jelly beans has a mass of 1450kg.If the jars mass is 245g.What is the mass of jelly beans
Answers
Answer:
1449.755 kilograms
Step-by-step explanation:
245 grams is .245 kilograms meaning that in order to get the answer you would need to subtract 1450 by .245 which is 1449.755 which means that the mass of jelly beans would be 1449.755 kilograms
__•__=42
__+__=23
Can someone help me solve this?
Answers
Answer:
21 * 2 = 42
21 + 2 = 23
Step-by-step explanation:
well I know that 6 * 7 = 42 so I’m assuming that’s correct
Then 11 + 12 = 23 it could be the answer I’m not positive for this one though.
The first one should be correct.
Maybe try
21 * 2 = 42
21 + 2 = 23
Write the equation of the line that passes through (4, 2) and is parallel to the line y = 2x – 1.
Answers
Answer:
Step-by-step explanation:
We will look for a line that has the general form of y = mx + b, where m is the slope and b the y-intercept (the value of y when x = 0).
A line parallel to y=2x-1 will have the same slope, 2.
We can write y = 2x + b for the new line. We need to find b. We can use the given point in this equation and solve for b:
y = 2x + b
2 = 2(4) + b for (4,2)
2 = 8 + b
x = -6
The parallel line to y=2x-1 that goes through point (4,2) is:
y = 2x-6
See the attached graph.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to write the equation of the line that passes through (4, 2) and is parallel to y=2x-1.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Parallel lines have the same slope.Since the slope of the given line is 2, the slope of the line parallel to this one is also 2.
Now, figure out the y-intercept, c:y=2x+c
We're given a point: (4, 2).Where: 2 is the y-coordinate of the point, and 4 is the x-coordinate.
Now, substitute 2 for y and 4 for x:
[tex]\longmapsto\sf{2=2(4)+c}[/tex]
Simplify!
[tex]\longmapsto\sf{2=8+c}[/tex]
Subtract 8 from both sides of the equal sign:
[tex]\longmapsto\sf{2-8=c}[/tex]
[tex]\longmapsto\sf{-6=c}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
the distance between dakshes's house and his school is 7 km.how many kilometers does he have travel in 6 days
Answers
Answer:
84km
Step-by-step explanation:
He has to travel 7 km in the morning to school and 7 km in the afternoon to home. 7km x 2 = 14km/day
He's making this trip 6 days a week: 6 days x 14km/day = 84km
7km x 2/day x 6 days = 84km
What is the solution to this Equation?
2(5x+8) = 6x+20
A. X = -1
B. X=9
C. X = -9
D. x = 1
Answers
Answer:
D(x=1).
Step-by-step explanation:
2(5x+8)=6x+20
10x+16=6x+20
10-6x+16=6x-6x+20
4x+16=20
4x+16-16=20-16
4x=4
4x/4=4/4
x=1
The solution to this equation is x = 1
Given the equation, we apply the distributive property.
That is, let's multiply the terms:2( 5x + 8 ) = 6x + 20
10x + 16 = 6x + 20
Now we will subtract the terms on both sides of the sentence:10x - 6x = 20 - 16
4x = 4
Finally, let's divide the second to the first term:x = 4 ÷ 4
x = 1
Therefore, the value of this equation is x = 1
Help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeee.
Answers
Answer:
it's 8
Step-by-step explanation:
the lil hand is on the 8 and the big hand is on the 12
Answer:
The time is 8:00 but with out a question im not sure what your asking
Step-by-step explanation:
y varies inversely as x. If y=4 when x=15, find y when x=12
Answers
The value of y given the inverse relationship is 5.
What is the value of y?If two variables vary inversely, as one variable increases, the other decreases in value.
The equation that is used to represent inverse relationship is:
y = k/x
Where k is the constant of proportionality
k = yx
k = 4 x 15 = 60
y = 60 / 12
y = 5
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can i have help with this please
Answers
Answer:
B) 7r² - r -1
Step-by-step explanation:
(3r² + 7r + 1) + (4r² - 8r - 2)
1. Remove unnecessary parentheses
3r² + 7r + 1 + 4r² - 8r - 2
2. Combine like terms (ex: r and -2r, n and 4n)
7r² - r -1
Therefore, the correct answer is B.
Hope this helps!
Answer: Heyaa! ~
Your Answer is... 7r²− r −1, Which is B.
Step-by-step explanation:
Subtract the numbers, And then combine like terms,
Solution: 7r²− r −1
Hopefully this helps you! ^
Is y=2x-3 a funtion?
Answers
Answer:
yes
Step-by-step explanation:
Yes.
The graph of y = 2x - 2 is a straight line sloping up to the right.
It passes the vertical line test, so it is a function.
The graph shows the quadratic function f, and the table shows the quadratic function g.
x -5 -4 -3 -2 -1 0 1
g(x) 10 7 6 7 10 15 22
A.
The functions f and g have the same axis of symmetry and the same minimum values.
B.
The functions f and g have different axes of symmetry and different minimum values.
C.
The functions f and g have the same axis of symmetry, but the minimum value of f is greater than the minimum value of g.
D.
The functions f and g have the same axis of symmetry, but the minimum value of f is less than the minimum value of g.
Which statement is true?
Answers
Analyzing the quadratic functions, it is found that the correct option is D. The functions f and g have the same axis of symmetry, but the minimum value of f is less than the minimum value of g.
How to analyze the function?Looking at the graph, Function f has a minimum value of 1 at x = -3. Hence, the axis of symmetry is x = -3.
Function g has a minimum value of 6 at x = -3. Hence, the axis of symmetry is also x = -3.
Therefore, the functions f and g have the same axis of symmetry, but the minimum value of f is less than the minimum value of g.
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