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
ioda
1 year ago
10

Please explain how they plugged the removable discontinuity in this question.

Mathematics
1 answer:
kondor19780726 [428]1 year ago
8 0

In the limit

\displaystyle \lim_{x\to c} f(x)

we're interested in the value that f(x) converges to as x gets closer to c. So in fact x\neq c.

In the given example, f(x) is factorized to reveal a common factor of x-1 in the numerator and denominator. We have x\neq1 if x\to1, so x-1\neq0 so we can simplify

\dfrac{x-1}{x-1} = 1

and *remove* the discontinuity.

Then

\displaystyle \lim_{x\to1} \frac{2(x-1)}{(x+1)(x-1)} = \lim_{x\to1} \frac2{x+1} = \frac2{1+1} = 1

You might be interested in
Two angels are supplementary. The measure of the large angle is four more than three times the measure of the small angle. Find
sashaice [31]

Answer:

The measure of the two supplementary angles is

Small angle = x = 44°

Large angle = y = 136

Step-by-step explanation:

Supplementary angles are two angles whose measures add up to 180° .

Let

Small angle = x

Large angle = y

x + y = 180°.... Equation 1

The measure of the large angle is four more than three times the measure of the small angle

Hence: y = 4 + 3x

We substitute 4 + 3x for y in Equation 1

x + 4 + 3x = 180°

4x + 4 = 180°

4x = 180° - 4

4x = 176

x = 176/4

x = 44°

Solve for y

y = 4 + 3x

y = 4 + 3(44)

y = 4 + 132

y = 136°

Therefore, the measure of the two supplementary angles is

Small angle = x = 44°

Large angle = y = 136

5 0
2 years ago
A teacher has 36 students who were randomly assigned to 6 rows of 6 desks. She wants to survey the students
ivanzaharov [21]

Answer:

A

Step-by-step explanation:

Edge 2021

5 0
3 years ago
According to the US department of labor, total employment is expected to increase from 146 million in 2000 to 168 million in 201
saveliy_v [14]

Answer:

The percent increase in the employment from the year 2000 to year 2010 is 15.07\%.

Step-by-step explanation:

Given:

Employment in the year 2000 =146 million.

Employment in the year 2010 =168 million.

To find: The percent increase in the employment.

Solution: We have,

Employment in the year 2000 =146 million.

Employment in the year 2010 =168 million.

Increase in employment =168-146=22 million.

Percent increase =\frac{\textrm{Increase in employment}}{\textrm{Original employment}}\times100\%

Percent increase =\frac{22}{146}\times100\%=15.07\%

Hence, the percent increase in the employment from the year 2000 to year 2010 is 15.07\%.

3 0
3 years ago
What is the solution to the equation 3/<br> x+4+3/2x+8 = 0?
mixas84 [53]

Answer:

X= -4

Step-by-step explanation:

^ you have to isolate the radical than raise each side to the power of its index which gets you

x= -4

5 0
2 years ago
Can some one help me on this
Vilka [71]
28 divided by 4 = 7
so do 7 * 5 which is 35 so they make 35 cookies in 5 seconds
4 0
2 years ago
Other questions:
  • Jim Lee received his bank statement from Bayne Bank indicating a balance of $7,980. Lee's checkbook showed a balance of $6,800.
    6·1 answer
  • What is the alt code for the division sign? 50 points
    7·2 answers
  • What is 2% written as a fraction in simplest form
    10·2 answers
  • Calculate the IRR if the power company gets a fixed feed-in tariff of $0.25/kWh, for 20 years and the salvage value of the plant
    11·1 answer
  • FP!!<br><br> what is 300 + 50
    9·2 answers
  • 11-12
    12·1 answer
  • Which value would not be part of the domain of the inverse of the given relation?
    8·1 answer
  • avery brought 10 cupcakes to the bakery she wanted to order 10 cupcakes does she have enough money show your work and explain ​
    8·2 answers
  • Six friends share 4 apples equally. How much apples does each friend friend get?​
    9·2 answers
  • Find the equation of the linear function represented by the table below in slope-
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!