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
Burka [1]
3 years ago
9

plain why the function is discontinuous at the given number a. (Select all that apply.) f(x) = x2 − 2x x2 − 4 if x ≠ 2 1 if x =

2 a = 2
Mathematics
1 answer:
ElenaW [278]3 years ago
4 0

Answer with Step-by-step explanation:

We are given that

f(x)=\left\{\begin{matrix}\dfrac{x^2-2x}{x^2-4}&,if\ \ x\neq 2 \\ 1&,if\ \ x=2\end{matrix}\right.

We have to explain that why the function is discontinuous at x=2

We know that if function is continuous at x=a then LHL=RHL=f(a).

f(x)=\frac{x(x-2)}{(x+2)(x-2)}=\frac{x}{x+2}

LHL=Left hand limit when x <2

Substitute x=2-h

where h is small positive value >0

\lim_{h\rightarrow 0}f(x)=\lim_{h\rightarrow 0}\frac{2-h}{2-h+2}

\lim_{h\rightarrow 0}\frac{2-h}{4-h}=\frac{2}{4}=\frac{1}{2}

Right hand limit =RHL when x> 2

Substitute

x=2+h

\lim_{h\rightarrow 0}f(x)=\lim_{h\rightarrow 0}\frac{2+h}{2+h+2}=\lim_{h\rightarrow 0}\frac{2+h}{4+h}

=\frac{2}{4}=\frac{1}{2}

LHL=RHL=\frac{1}{2}

f(2)=1

LHL=RHL\neq f(2)

Hence, function is discontinuous at x=2

You might be interested in
the measures of the side of a triangle are 4√2 cm, 4√2 cm qnd 8√2 cm. what is the perimeter of the triangle?​
spin [16.1K]

Answer:

16\sqrt{2}

Step-by-step explanation:

Add up all the sides to get the perimeter:

4\sqrt{2} + 4\sqrt{2} +8\sqrt{2} = 16\sqrt{2}

8 0
2 years ago
I need help solving this equation
solmaris [256]

Answer:

-765

Step-by-step explanation:

-2-7 * 109

-2 - 763

-765

4 0
3 years ago
Read 2 more answers
12. The $60 selling price of a camera is the cost<br> increased by twice the cost. Find the cost.
prisoha [69]

Answer: Assuming you mean that the original cost was doubled and now equals $60, the camera costed $30. Assuming the camera's price has been doubled from $60, it is $120. The wording is a bit unclear, so I'm giving you both answers.

Step-by-step explanation: To find half of the price of $60, simply divide it by 2, which gives you $30.

3 0
3 years ago
A sporting goods store pays $180 for a rubber raft. The percent markup is 40%. What is the raft's selling price?
o-na [289]
\$180 \times 1.40 = \$252
5 0
3 years ago
A _____ is accepted to be true without proof, while a _____ is an assertion that can be proven using the rules of logic.A.theore
Luba_88 [7]

Answer:

  C.  postulate; theorem

Step-by-step explanation:

While a "given" is taken as true without proof, and a "problem" sometimes involves an assertion that can be proven, the answer choices involving these terms are not correct here.

The dictionary definitions of "postulate" and "theorem" apply. It is useful to learn the meaning of these terms so you can understand problems and descriptions that use them.

3 0
3 years ago
Other questions:
  • A TV costs £800 plus a VAT if 20%<br> What us the total cost of the TV?
    5·2 answers
  • 10m-3(2m-9)=9(m-1)+1
    11·1 answer
  • 3621 ×4 help me on this please
    15·2 answers
  • A financial analyst has determined that there is a 23 % probability that a mutual fund will outperform the market over a 1 -year
    6·1 answer
  • 9 gal/s=_____qt/min
    9·1 answer
  • Hey ya'll, my assignment asked me.....Evan spent 20 hours doing homework last week. This week he spent 25 hours doing homework.
    5·2 answers
  • Which of these can be classified as irrational numbers? explain.
    15·1 answer
  • Help pleasee! i have to turn this in soon
    10·1 answer
  • You are constructing a copy of . You choose a point, C, as one of the endpoints for the new line segment. What is the next step
    12·1 answer
  • If 1/2 a number is 5 more than 1/7 of that number, what is the number?​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!