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
Triss [41]
3 years ago
11

HELP!!!!!!!!!! AP CALCULUS AB

Mathematics
2 answers:
raketka [301]3 years ago
8 0

Answer:

\lim_{x \to 5^{-}} f(x)= 54

\lim_{x \to 5^{+}} f(x) = -17

Step-by-step explanation:

+ means we are approaching from the right

- means we are approaching from the left

We are given that if x < 5, it is x² + 5x + 4

So to find \lim_{x \to 5^{-}} f(x) we would plug in 5 into that piecewise function part:

5² + 5(5) + 4 = 54

We would be approaching y = 54 if we approach from the left.

We are given that x > 5, it is -4x + 3

So to find \lim_{x \to 5^{+}} f(x) we would plug in 5 into that piecewise function part:

-4(5) + 3 = -17

We would approach y = -17 if we approached from the right.

Shtirlitz [24]3 years ago
5 0

Answer:

\lim_{x \to 5^-}f(x)=54\\\lim_{x \to 5^+}f(x)=-17

Step-by-step explanation:

So, we have the function:

f(x)=x^2+5x+4,x

And we want to show that this has a jump discontinuity.

As directed, calculate the limit at x=5 from the left and from the right. Thus:

\lim_{x \to 5^-}f(x)

To calculate this, since we're coming from the left, x is less than 5. So, use the first equation:

\lim_{x \to 5^-}f(x)\\= \lim_{x \to 5^-}(x^2+5x+4)\\

Use direct substitution:

=(5)^2+5(5)+4\\=25+25+4\\=54

Thus, as the limit approaches f(5) from the left, the function approaches 54.

Now, calculate the limit at x=5 from the right. Since we're coming from the right, use the third equation:

\lim_{x \to 5^+}f(x)\\= \lim_{x \to 5^+}(-4x+3)

Direct substitution:

(-4(5)+3)\\=-20+3\\=-17

Thus, as the limit approaches f(5) from the <em>right</em>, the function approaches -17.

As you can picture, there's a huge gap between y=54 and y=-17. The limits are not equal and both of the limits do exist. Thus, we have jump discontinuity.

You might be interested in
On Monday,it took Helen 3 hours to do a page of science homework exercises.The next day she did the same number of exercises in
Blababa [14]

Answer:

It's 3/2p!

Step-by-step explanation:

Because Helen do the same number of exercises on 2 days, the time to do and the average rate are  inversely proportional!

So, if on Monday, Helen's average rate is p then on the next day, her average rate is:

p × 3 ÷ 2 = \frac{3p}{2}

=3/2p

Brainliest?

3 0
3 years ago
Please help ASAP 15 points
klio [65]

Answer:

B

Step-by-step explanation:

The answer is B because it tells you the letter atound triangle.

5 0
3 years ago
Read 2 more answers
In the equation Y+8=2 what does y=?
Jet001 [13]
Y = -6 hope this helps
5 0
3 years ago
Medicine can be described as
larisa [96]

Answer:

C) a type of drug used to cure, prevent, or treat illness or discomfort.

5 0
3 years ago
Read 2 more answers
If f(x)=|x+2| is changed to g(x)=3f(x)+4, how is the graph of the function transformed?
frozen [14]

Answer:

download photomath it will help u with any type of math

3 0
3 years ago
Other questions:
  • In triangle ABC, m a = 45 m b =65 and a = 15.05. Use the law of sines to find b. Round your answer to the nearest tenth.
    10·2 answers
  • Wat is the inequality of n+6&gt;-3
    5·2 answers
  • 6)
    12·1 answer
  • There are 7,500 shares of $10 par value participating 9 percent preferred stock outstanding, and 32,500 shares of common stock o
    12·1 answer
  • 9) Write an expression which represents the **sum** of (7x-5y) and (-8x-8y) in<br> simplest terms
    9·2 answers
  • Students in 4th and 5th grade took a survey regarding their favorite cafeteria food. What percent of the students selected pizza
    6·1 answer
  • What is the difference between 3^2 (three raised to the power of two) and 3(2) (three times two)?
    10·2 answers
  • Write 0.2 as a fraction in simplest form.
    15·2 answers
  • Which point is located at -1 3/4 on the vertical number line?
    8·1 answer
  • Frank has $156.87 he spends $21.58 to buy a gift for his sister he also earned $45.50 how much does he have now?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!