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
tangare [24]
3 years ago
13

I don’t know how to do this

Mathematics
1 answer:
stich3 [128]3 years ago
4 0

To check for continuity at the edges of each piece, you need to consider the limit as x approaches the edges. For example,

g(x)=\begin{cases}2x+5&\text{for }x\le-3\\x^2-10&\text{for }x>-3\end{cases}

has two pieces, 2x+5 and x^2-10, both of which are continuous by themselves on the provided intervals. In order for g to be continuous everywhere, we need to have

\displaystyle\lim_{x\to-3^-}g(x)=\lim_{x\to-3^+}g(x)=g(-3)

By definition of g, we have g(-3)=2(-3)+5=-1, and the limits are

\displaystyle\lim_{x\to-3^-}g(x)=\lim_{x\to-3}(2x+5)=-1

\displaystyle\lim_{x\to-3^+}g(x)=\lim_{x\to-3}(x^2-10)=-1

The limits match, so g is continuous.

For the others: Each of the individual pieces of f,h are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.

You might be interested in
You are given 6 color cards: 1 red, 2 blue, 3 green. As you draw a card, YOU WILL KEEP IT. What is the probability of drawing a
nikitadnepr [17]

Answer:

3/6, 2/5, 0/5

Step-by-step explanation:

4 0
3 years ago
Find the distance between a point (–7, –19) and a horizontal line at y = 3.
Lelechka [254]
Try to use this rule and use those 2 given points——-

(-7,-19) (0,3)

8 0
3 years ago
If
Dominik [7]

Answer:

SQR = 60

Step-by-step explanation:

BISECTS both angles are equal

RQS = SQP

5x+10=7x-10

20=2x

10=x

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

5(10)+10=50+10=60

60 + 60 =120

4 0
3 years ago
Two lines that intersect to form right angle are called
Sergio039 [100]

Answer:

perpendicular

Step-by-step explanation:

When 2 lines intersect at any point, not just in the middle of each (that has nothing to do with it), and they meet to form right angles, the lines are perpendicular to one another and their slopes are opposite reciprocals.

4 0
3 years ago
-8,-1,6,13 what the next three numbers
kobusy [5.1K]
20,27,34

The common difference is 7
7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the mean and mode of the data set shown below? {2, 4, 5, 6, 8, 2, 5, 6}
    15·1 answer
  • Solve: 3m - 2.4 = 6.6
    10·2 answers
  • Which expression is equivalent to sin(1.8x) sin(0.5x)?
    15·1 answer
  • One grain of sand = 7*10 to the power of -5 how many grains of sand are in 6300 kg
    11·1 answer
  • WILL GIVE BRAINLYEST
    7·1 answer
  • Multiply. write the result in scientific notation. (2.3x10^1)(7x10^6)
    13·2 answers
  • Which point is a reflection of (5, 3) across the xaxis ?
    11·2 answers
  • Algebra help!!! giving brainliest and you’ll get 20 points rather than 10!!! (asap please)
    9·2 answers
  • I added a picture : Determine which of the lines, if any, are parallel or perpendicular. Explain.
    9·1 answer
  • A store has 2000 grocery bags to give away as part of its grand opening. The store is handing out 150 bags per hour. In how many
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!