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
QveST [7]
3 years ago
6

Discontunuity of f(x) = x^2 plus 2x over x plus 2

Mathematics
1 answer:
Lina20 [59]3 years ago
8 0

Answer:

When we have a function like:

f(x) = \frac{g(x)}{h(x)}

This function will have a discontinuity only if it diverges, and a divergence can happen when the denominator is equal to zero and the numerator is different than zero.

In this case, we have the equation:

f(x) = \frac{x^2 + 2*x}{x + 2}

Here the denominator is:

h(x) = x + 2

This is equal to zero when:

x + 2 = 0

x = -2

Now we need to see what happens with the numerator when x = -2

g(-2) = (-2)^2 + 2*(-2) = 0

Is equal to zero.

Then we need to see the limit when x -> -2, and use the L'Hopital theorem.

\lim_{x \to \ - 2} \frac{x^2 + 2*x}{x + 2}

Because we have zero over zero at that point, we need to look at the quotients of the derivatives of both numerator and denominator.

\lim_{x \to \ - 2} \frac{2*x+ 2}{ 2} = \frac{2*-2 + 2}{2} = -1

Then the function does not diverge, then the function has no discontinuity.

We also could look at the graph of f(x) to see it:

Our function is a linear function, and this is because the numerator is x times the denominator, then the function is:

f(x) = x.

You might be interested in
Stephanie is making 1 1/2 batches of cookies using 2 3/4 cup sugar. How much sugar total?()
storchak [24]

Answer:

33/8 or 4 1/8 simplified.

6 0
2 years ago
Draw 2 squares. The first one should have an area of 12 square units.The second one should have an area that is DOUBLE that of t
statuscvo [17]

Step-by-step explanation:

Given the information:

  • 1st square:  12 square units
  • 2nd square: DOUBLE that of the first square = 2*12 = 24 square units

From that, we can determine the length of the side in each square:

1/ x^{2} = 12

<=> x = 2\sqrt{3}

2/ a^{2} = 24

<=> a = 2\sqrt{6}

Please have a look at the attached photo.

Hope it will find you well.

6 0
2 years ago
Math problem I need help giving brainlist
Liono4ka [1.6K]

Answer:

x = 28

Step-by-step explanation:

7(8 - x) = -5x

56 - 7x = -5x                 Distribute 7 to the parenthesis

56 = 2x                         Add -7x to both sides

28 = x                           Divide 2 to both sides

3 0
3 years ago
Read 2 more answers
Use special right triangles.<br> Find the exact value of x and y.<br> 18<br> 30°<br> X = ?<br> y = ?
spin [16.1K]

Answer:

Step-by-step explanation:

j

8 0
2 years ago
Read 2 more answers
28.4.2 Test (CST): Transformations, Congruence, and Similarities, Part 2
frez [133]

Answer:

R'(2,4)

Step-by-step explanation:

When doing translations you subtract or add within the coordinates like a normal problem.

If it helps you, write it as seperate equations like:

1-1 and 5-1

Hope that helps ✓

8 0
2 years ago
Other questions:
  • (1.8 * 10^2) * (5 * 10^2)
    14·1 answer
  • Find the x-coordinates of the points where the graph crosses the x-axis.<br> y = (x - 3)(x + 8)
    7·1 answer
  • A dilation is an example of a similarity transformation.
    13·2 answers
  • I need help getting started
    13·2 answers
  • In a class there are 25 students 15 are boys what percentage are girls​
    10·1 answer
  • PLEASE HELP ILL GIVE BRAINLEST
    7·1 answer
  • HELP PLS IM BEING TIMED <br><br><br> Which graph represents y as a function of x?
    11·2 answers
  • Need help with this
    9·1 answer
  • Find x and y. <br><br> pls pls help
    12·1 answer
  • The blood platelet counts of a group of women have a boll-shaped distribution with a mean of 261.1 and a standard deviation of 6
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!