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
The area of a rectangle is 30 square root 3750 square inches, and the length is 3 square root 250 inches what is the width of th
Ann [662]

Answer:

width=10\sqrt{15}\ in

Step-by-step explanation:

-A rectangle's area is given by:

A=lw\\\\l=length\\w=width

Given A=30\sqrt{3750} and l=3\sqrt{250}, we substitute in the formula to solve for the width as follows:

A=lw\\\\30\sqrt{3750}=3\sqrt{250}\times w\\\\w=\frac{30\sqrt{3750}}{3\sqrt{250}}\\\\w=10\frac{\sqrt{3750}}{\sqrt{250}}\\\\=10\times \sqrt{\frac{3750}{250}}\\\\=10\sqrt{15}\ in

Hence , the rectangle's width is 10\sqrt{15}\ in

6 0
3 years ago
Explain the difference between prime and composite numbers
Fed [463]
Prime only has two factors one and its self a composite number has more factor than one and its self
exsample:     12 -  1,2,3,4,6,12  = 12 is a composite number
                       7  -  1,7                 =prime number 
4 0
3 years ago
Eben, an alien from the planet Tellurango, kicks a football from field level. The equation for the football’s height in meters,
Luden [163]

<span>The maxima of a differential equation can be obtained by getting the 1st derivate dx/dy and equating it to 0.</span>

<span>Given the equation h = - 2 t^2 + 12 t       , taking the 1st derivative result in:</span>

dh = - 4 t dt + 12 dt

<span>dh / dt = 0 = - 4 t + 12   calculating for t:</span>

t = -12 / - 4

t = 3 s

Therefore the maximum height obtained is calculated by plugging in the value of t in the given equation.

h = -2 (3)^2 + 12 (3)

h = 18 m

This problem can also be solved graphically by plotting t (x-axis) against h (y-axis). Then assigning values to t and calculate for h and plot it in the graph to see the point in which the peak is obtained. Therefore the answer to this is:

<span>The ball reaches a maximum height of 18 meters. The maximum of h(t) can be found both graphically or algebraically, and lies at (3,18). The x-coordinate, 3, is the time in seconds it takes the ball to reach maximum height, and the y-coordinate, 18, is the max height in meters.</span>

6 0
3 years ago
Which of the following is the solution of –6x – 17 = 19?
natita [175]

   -6x - 36  =   -6 • (x + 6) 

                   x = -6
<span>
</span>

6 0
3 years ago
Read 2 more answers
How do I solve y+5x=2;-1,0,1 ?
vfiekz [6]
Plug is the number try one and see if it equals and solve for y get y on one side
5 0
3 years ago
Other questions:
  • Walt and Hank collect quarters from different states. Walt collected q quarters. Hank collected four fewer quarters than Walt. T
    15·1 answer
  • How would I set up the equation to find mRQS on this circle?
    6·1 answer
  • Choices for Question #1:
    8·1 answer
  • Carlos is using a number line to add another integer to –4. He begins by showing –4 on the number line, as shown below. Carlos a
    11·1 answer
  • The graph of the line with the equation y = 1/2 * x + 4 crosses the x-axis at which of the following
    12·1 answer
  • What is the value of x?<br> 60<br> –16<br> 120<br> 16
    12·1 answer
  • PLEASE HELP, WILL GIVE BRAINLIEST!!
    8·1 answer
  • Which number has a value between -8.423 and -8.395?
    9·1 answer
  • What is the answer to this?
    14·1 answer
  • How much would each starburst weigh if 3 starburst weigh 1 ounce?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!