For what value of the number k is the following function differentiable at x=2
f(x) = {2x + 1 if x<2
k x=2
3x-1 x>2}

Answers

Answer 1

Answer:

For f(x) to be differentiable at 2, k = 5.

Step-by-step explanation:

For f(x) to be differentiable at x = 2, f(x) has to be continuous at 2.

For f(x) to be continuous at 2, the limit of f(2 – h) = f(2) = f(2 + h) as h tends to 0.

Now,

f(2 – h) = 2(2 – h) + 1 = 4 – 2h + 1 = 5 – 2h.

As h tends to 0, lim (5 – 2h) = 5

Also

f(2 + h) = 3(2 + h) – 1 = 6 + 3h – 1 = 5 + 3h

As h tends to 0, lim (5 + 3h) = 5.

So, for f(2) to be continuous k = 5


Related Questions

Help! I think this is correct but im unsure

Answers

The answer is the second option you are correct !
Yeah your right !!!!!!

what is the gradient?

Answers

Answer:

[tex] \frac{3}{2} [/tex]

Step-by-step explanation:

hi thereas we know gradient of Graf=

[tex] \frac{∆y}{∆x} [/tex]

[tex] \frac{3}{2} [/tex]

Find the value for x and y for the triangle. Show work.

Answers

Answer:

tan60=p/b

tan60=12/x

x=37.5

now taking sin

sin60=p/h

sin60=12/y

y=(-40) but as length can be negative so

y=40

translate into mathematical phrase.the weight (w) is more than 2kg​

Answers

Answer:

w>2kg

Step-by-step explanation:

the weight is greater than 2kg.

Chuck is taking his kids to the store to buy new converse shoes. he is given a choice of high tops or low tops. They may also choose from the colors red, gray, black, or pink.

What is the probability that his kids will choose a low top shoe that is gray or pink?


A. 1/4

B. 1/2

C. 1/3

D. 3/4

Answers

Answer:

B. 1/2

Step-by-step explanation:

The kids are given 4 options (grey, pink, red, black)

pink and grey are 2 options out of the 4 so 2/4

or 1/2 probability that they will choose the grey or pink shoes

plz mark me brainliest

HURRY PLEASE On a coordinate plane, point A is 2 units to the left and 5 units up. Point B is 5 units to the right and 5 units up. What is the distance between the points? Point A is located at the point . Point B is located at the point . The distance between the points is units.

Answers

Answer:

point A is located at (-2,5) and point B is located at point (5,5), the distance between the points is 7 units. hope this helps!

The distance between the points will be 7 units. Point A is located at the point (-2, 5). Point B is located at the point (5, 5).

What is distance between points?

The formula of distance between two points is A(x₁, y₁) and B(x₂, y₂) is given by: [tex](A,B) = \sqrt{( x_{2} - x_{1} )^2 + ( y_{2} - y_{1})^2}[/tex]

We have,

Point A (-2, 5) and Point B (5, 5).

i.e.

x₁ = -2,  x₂ = 5 and

y₁ = 5,   y₂ = 5

Now,

Using the above mentioned formula of distance,

i.e.

Distance [tex](A,B) = \sqrt{( x_{2} - x_{1} )^2 + ( y_{2} - y_{1})^2}[/tex]

So,

Substituting values,

Distance [tex](A,B) = \sqrt{(5-(-2) )^2 + ( 5-5)^2}[/tex]

Now, simplify,

Distance [tex](A,B) = \sqrt{(7)^2 + 0}[/tex]

We get,

Distance [tex](A,B) = 7[/tex]

So, the distance between AB is 7 units.

Hence, we can say that the distance between the points will be 7 units. Point A is located at the point (-2, 5). Point B is located at the point (5, 5).

To know more about distance between the points click here

https://brainly.com/question/15958176

#SPJ2

the ratio of strawberries to grapes in the fruit salad is 3:9. the ratios of strawberries to honey dew is 6:14. if there 36 grapes. how many strawberries?

Answers

Answer:

12 strawberries

Step-by-step explanation:

Represent strawberry with S, grape with G and honeydew with H

Given

[tex]S : G = 3 : 9[/tex]

S : H = 6 : 14

Required

Solve for S when G = 36

To do this, we make use of the first ratio

[tex]S : G = 3 : 9[/tex]

Substitute 36 for G

[tex]S : 36 = 3 : 9[/tex]

Convert to fractions

[tex]\frac{S}{36} = \frac{3}{9}[/tex]

[tex]\frac{S}{36} = \frac{1}{3}[/tex]

Multiply both sides by 36

[tex]36 * \frac{S}{36} = \frac{1}{3} * 36[/tex]

[tex]S = \frac{1}{3} * 36[/tex]

[tex]S = \frac{36}{3}[/tex]

[tex]S = 12[/tex]

Hence, there are 12 strawberries

I don't know if I'm right or not. I think it's C, but I'm not too sure.

Answers

Answer:

its c

Step-by-step explanation:

Answer:

Ya its c

Step-by-step explanation:

It's correct u can cliuck or do it without any fear best of luck

Find the area of the parallelogram shown below.
3
6
square units
Stuc. TAI

Answers

Answer: 18

Step-by-step explanation:

Area of parallelogram: b × h

3 × 6 = 18

Hope this helped! :3

Louis and Ricardo took a timed a reading test, and the results below show the number of words each student can read per minute which student reads at a faster rate ?

Answers

Answer:

Louis reads faster

Step-by-step explanation:

See attachment for complete question.

The table represents Louis data while the graph represents Ricardo's data.

To solve this question, we simply calculate the slope of the table/graph,

The slope (m) is calculated by:

[tex]m=\frac{y_2 - y_1}{x_2 - x_1}[/tex]

For Louis:

From the table, we pick any corresponding x and y values

[tex](x_1,y_1) = (2,436)[/tex]

[tex](x_2,y_2) = (6,1308)[/tex]

[tex]m_1 = \frac{1308 - 436}{6-2}[/tex]

[tex]m_1 = \frac{872}{4}[/tex]

[tex]m_1 = 218[/tex]

For Ricardo:

From the graph, we pick any corresponding x and y values

[tex](x_1,y_1) = (2,300)[/tex]

[tex](x_2,y_2) = (6,900)[/tex]

[tex]m_2 = \frac{900- 300}{6-2}[/tex]

[tex]m_2 = \frac{600}{4}[/tex]

[tex]m_2 = 150[/tex]

So, we have:

Louis: [tex]m_1 = 218[/tex]

Which means 218 words per minutes

Ricardo: [tex]m_2 = 150[/tex]

Which means 150 words per minutes

I Need help pls!
What is 75% of 800?
A; 9 3/8
B; 10.66

Answers

Answer:

it's 600

Step-by-step explanation:

that's not an option there but...

10% of 800 is 80

5% of 800 is 40

80 × 7 = 560

560 + 40 = 600

Which is the correct answer?

(Note): (if you give me a silly or absurd answer I will report you)​

Answers

Step-by-step explanation:

Since N ≡ 0 (mod 2) and N ≡ 0 (mod 3),

N ≡ 0 (mod (2*3)) ≡ 0 (mod 6).

Hence when N is divided by 6,

the remainder is 0. (A)

GIVING BRAINLIEST

In the coordinate plane, the points A (7, 5), B(-10, -9), and C(4, - 11) are reflected over the x-axis to the points A, B', and C', respectively. What are
the coordinates of A', B', and C'?

Answers

Answer:

A (-7,5) .  B (10,9) .      C (-4,-11

Step-by-step explanation:

What is 9 square foot in square feet ?

Answers

9 square feet is 81 feet

83, 694 ,357 expanded notation using descending order ​

Answers

Answer:

Step-by-step explanation:

eighty three, three hundred and fifty seven,six hundred and ninty four

80+3=83,300+50+7=357,600+90+4=694

This is the order.

Hope this helps!

Woman .......Kam hir​

Answers

What did he sayyyyyyy

Shiloh needs to randomly select one of the six days between Sunday and Friday. Which simulation tools could she use in this situation?

((( MULTIPLE ANSWERS))



A-a spinner divided evenly into 12 sections, with each section a different color

B-two coins

C-a six-sided number cube

D-a bag containing 12 chips in two different colors, with six of each color

E-two full suits from a standard deck of cards

Answers

Answer:

The correct answer is C. She could use a six-sided number cube.

Step-by-step explanation:

Since Shiloh has 6 options from which to choose a unique alternative, it can be stated that her eligibility ratio is 1/6. Thus, since the dice has 6 numbers and only 1 will come up face up, the option of the dice is the most appropriate to make her decision.

On the other hand, the other options do not contemplate 6 possibilities but 12, 2, 12 and 13 possibilities respectively, with different possible alternatives, which does not give an equitable distribution of possibilities between each option.

Answer:

Behold!

Step-by-step explanation:

Steps to Solve:

-(2³)p + (-6p) = -112

Answers

Answer: p=8

Step-by-step explanation:(−23)(p)−6p=−112

−8p+−6p=−112

(−8p+−6p)=−112(Combine Like Terms)

−14p=−112

−14p=−112

−14p/−14 = −112/−14

p=8

Find the distance between the points (1.0) and (0.2)

Answers

YEH ITS WRONG SORRY DON'T REPORT ME!

the ratio of dogs to cats is 5 to 3, if there are 14 more dogs than cats, how many animals are there altogether?​

Answers

Answer:

35

Step-by-step explanation:

D/C=5/3, so 3D=5C. 14+C=D is the second equation, so now you can solve for each.

3D=5C, 14+C=D
D=(5/3)C
14+C=(5/3)C
14=(2/3)C
C=21

21+14=D=35

So there are 21 cats and 35 dogs, or 56 total animals.

1.

Ginger works at the local putt-putt golf course. Her

weekly wages, y, are $7.25 per hour, x, she works.

Which equation best represents this relationship?

Answers

Answer: The equation that best represent this relationship is y=7.25x

Step-by-step explanation:

Please help me due today?

Answers

7x - 1 = 4x + 8
3x = 9
x = 9

ABD
7(3) - 1
21 - 1
20

DBC
4x + 8
4(3) + 8
12 + 8
20

3x - 17 + x + 40 + 2x - 5 = 180
6x + 18 = 180
6x = 198
x = 33

3(33) - 17
99 - 17
82

33 + 40
73

2(33) - 5
66 - 5
61

please I need a solution

Answers

Answer:

EEEEEeeEEeEEEEEEEeEEEEEEEEEE eEEEEEEEEeEEEEeEeEeEEEEEeeeeeeeeEeeeeEeeeeEeeEeeeEeeEe a good day at work and I will

4/5 + 1/2 = ?
A 1 3/10
B 15/10
C 2 4/10
D 5/7

Answers

Answer:

13/10

Step-by-step explanation:

The right answer is A

Lesson 4 problem solving practice

Answers

Answer:

what is your question?

Step-by-step explanation:

integers between -1and -5​

Answers

-2, -3, -4.

an integer is a number that isn't a fraction. so literally any natural number like 1, 0, or -1. all integers.

What is the ordered pair for A’ if A(2,-3) is reflected over the x-axis?

Answers

Answer:

A´= (2, 3)

Step-by-step explanation:

PLEASE ANSWER ASAP!!!!!!!!!!!!!!!
Authors set a TONE or MOOD in literature by conveying an emotion or emotions through ________.

Answers

Answer:

Author's craft

Step-by-step explanation:

f dcsdfsxadszcdxsfaczdsadzxsaddesdxxedrdrdsqxd

write the equation of a line in standard form that has a slope of 3 and passes through the point (-2,4)

Answers

Answer: E) 3x - y = 2

Step-by-step explanation:

Standard form is Ax + By = C

Ax must be positive

Hope this helps <3

find the sum of 0.48 and 0.6

Answers

Answer: the sum is 1.08

Other Questions
It took Jeremy 1 minute and 20 seconds to complete one test problem. How long will it take him to complete 6 problems? Look at the picture and match easy 5th grade math 20 points!!!! I need help plz and thank you this is dueComputer technology is quickly becoming a staple course required for students, even in middle school. Explain why it might be important to learn how to use computers even if your career path is not in the Information Technology career cluster. PLEASE HELP This table models a linear function.x -8 -4 4 8y -1 0 2 3Enter the coordinates of the y-intercept in the boxes. What is the SI unit of mass?Select one:a.Ounceb.Newtonc.Poundd.Gram What is the answer for p^2-3p Which number is farther from 0: -3/4 or 5/8? The juice dispenser in the cafeteria holds 22 1/2 pints of juice. The glasses in the cafeteria only hold 1/4 of a pint of juice. How many full glasses can be served at breakfast?a.89b.4c.44 1/4d. 356 Who was the first scientist Heat Illnesspls help my school wants me to write a something but I have two choosesI could write it as a poem or as a story.which one should I pick? A pack of cinnamon-scented pencils sells for $7.00. What is the sales tax rate if the total cost of the pencils is $7.35? if PQ is reflected across the X-axis, what will be the coordinates of P'Q' repeated? Carbohydrate needs of student athletes vary depending on the individual and type of sport, but intakes of ______ g/day are recommended for most athletes. HELP ME PLEASE!! IAM BEING TIMED.I WILL GIVE YOU BRAINLIEST! Which option best corrects this sentence fragment? Along the narrow forest trail.A) Along the winding, narrow forest trail.B) Along the narrow forest trail, tiny wildflowers grew.C) Ferns and bushes along the narrow forest trail.D) At twelve o'clock, along the narrow forest trail. Which of the following best describes the main focus of Lincoln's speech?A. Remembering and respecting the Confederate deadB. Honoring Union dead and their sacrifice in order to inspire the public to support the war effortC. The pointlessness of historical memoriesD. Reimagining future national purposes20 POINTS What is the midpoint of the segment shown below? Which system of linear equations has the ordered pair (-2,8) as its solution?y - 2x = 12 and x - 2y = -18x 2y = 12 and y - 2x = -18y + 2x = 12 and x + 2y = -18x + 2y = 12 and y + 2x = -18