1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
likoan [24]
3 years ago
7

Find each x-value at which f is discontinuous and for each x-value, determine whether f is continuous from the right, or from th

e left, or neither.
f(x) = x + 9 if x < 0
e^x if 0 ≤ x ≤ 1
4 − x if x > 1
x = (smaller value)
continuous from the right, or continuous from the left, or neither
x = (larger value)
continuous from the right, or continuous from the left, or neither
Mathematics
1 answer:
fredd [130]3 years ago
7 0

Using continuity concepts, the answers are given by:

  • The function is right-continuous at x = 0.
  • The function is left-continuous at x = 1.

------------------------------------

A function f(x) is continuous at x = a if:

\lim_{x \rightarrow a^{-}} f(x) = \lim_{x \rightarrow a^{+}} f(x) = f(a)

  • If \lim_{x \rightarrow a^{-}} f(x) = f(a), the function is left-continuous.
  • If \lim_{x \rightarrow a^{+}} f(x) = f(a), the function is right-continuous.
  • For the given function, the continuity is tested at the points in which the definitions are changed, x = 0 and x = 1.

------------------------------------

At x = 0.

  • Approaching from the left, it is less than 0, thus:

\lim_{x \rightarrow 0^-} f(x) = \lim_{x \rightarrow 0} x + 9 = 0 + 9 = 9

  • Approaching from the right, it is more than 0, thus:

\lim_{x \rightarrow 0^+} f(x) = \lim_{x \rightarrow 0} e^x = e^0 = 1

  • The numeric value is:

f(x) = e^0 = 1

  • Since [tex]\lim_{x \rightarrow 0^+} f(x) = f(0), the function is right-continuous at x = 0.

------------------------------------

At x = 1.

\lim_{x \rightarrow 1^-} f(x) = \lim_{x \rightarrow 1} e^x = e^1 = e

\lim_{x \rightarrow 1^+} f(x) = \lim_{x \rightarrow 1} 4 - x = 4 - x = 3

f(1) = e^1 = e

  • Since [tex]\lim_{x \rightarrow 1^-} f(x) = f(1), the function is left-continuous at x = 0.

A similar problem is given at brainly.com/question/21447009

You might be interested in
Worth 10 points on chapter 5 test
charle [14.2K]

Answer:

What is the value of x.

If you know the value of x

then,

perimeter= x+12+7.71

and

if this traingle is an equilateral triangle

then,

area =½×7.71×x

In this all process you need to find x then all will be easy

Hope it helped you

If not then I am sorry for that

Bye

3 0
3 years ago
Exhibit B In order to determine whether or not there is a significant difference between the hourly wages of two companies, two
ser-zykov [4K]

Answer: c. 3.01

Step-by-step explanation:

The test statistic for difference between two population mean (when population standard deviation is known) is given by :

z=\dfrac{\overline{x}_1-\overline{x}_2}{\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}}

, where n_1 = Size of first sample

n_2 = Size of second sample

\overline{x}_1-\overline{x}_2 = Difference between two sample mean.

\sigma_1 = standard deviation for population 1.

\sigma_2 = standard deviation for population 2.

As per given , we have

n_1=80

n_2=60

\overline{x}_1=\$6.75

\overline{x}_2=\$6.25

\sigma_1=\$1

\sigma_2=\$0.95

Substitute these values in formula , we get

z=\dfrac{6.75-6.25}{\sqrt{\dfrac{(1)^2}{80}+\dfrac{(0.95)^2}{60}}}

z=\dfrac{0.50}{\sqrt{0.0275416666667}}

z=\dfrac{0.50}{0.165956821694}

z=3.0128318613\approx3.01

Hence, the value of the test statistic is <u>3.01</u>.

Hence, the correct option is c. 3.01 .

7 0
3 years ago
Add. *
Ann [662]

Answer:

31x³-60x²+7x-75

Step-by-step explanation:

(30x³-49x³+7x)+(50x³-60x²-75)

(-19x³+7x)+(50x³-60x²-75)

-19x³+50x³+7x-60x²-75

31x³-60x²+7x-75

3 0
3 years ago
The coach paid $246 for 12<br>basketball uniforms. What<br>is the unit price?​
kozerog [31]

The Unit Price is 20.5

4 0
3 years ago
The length of a store is 21 2/3 feet, and the area is 325 square feet, what is the width of the store?
Julli [10]
325 divided by area 21 2/3. always area divided by length
4 0
3 years ago
Other questions:
  • There are 76 boys in a sophomore class of 165 find the ratio
    5·1 answer
  • HELP QUICK PLEASEE THANKS
    9·2 answers
  • Solve for b2 in A = h ( b1 + b2 ), if A = 16, h = 4, and b1 = 3.
    11·2 answers
  • A ball is kicked upward with an initial velocity of 52 feet per second. The ball's height, h (in feet), from the ground is model
    13·1 answer
  • A jar contains 15 navy and 26 violet marbles. A marble is drawn at random. What is the probability that the marble is violet?
    5·2 answers
  • Smoe brought a bag of bird food that held 2 1/2 lbs. of food. He Fed Smoe Dog the same amount of food for each 12 days. How many
    12·1 answer
  • Susannah made the line plot below to show the distances she hiked each day in the past two weeks.
    9·2 answers
  • The equati...
    13·2 answers
  • The different between three times a number and five is equal to the product of four times the number increased by two.
    14·1 answer
  • .
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!