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
natulia [17]
3 years ago
15

Let f be the function defined as follows:

Mathematics
1 answer:
katen-ka-za [31]3 years ago
7 0

With f defined by

f(x)=\begin{cases}|x-1|+2&\text{for }x

in order for it to be continuous at x=c, we require

\displaystyle\lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)=f(c)

(i) If a=2 and b=3, then f(1)=2(1)^2+3(1)=5 and

\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1}|x-1|+2=2

\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1}2x^2+3x=5

The limits don't match, so f is not continuous at x=1 under these conditions.

(ii) To establish continuity at x=1, we'd need the limit as x\to1 from the right to be equal to the limit from the left, or

\displaystyle\lim_{x\to1}ax^2+bx=\lim_{x\to1}|x-1|+2\iff a+b=2

(iii) We have f(2)=0 and

\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2}ax^2+bx=4a+2b

\displaystyle\lim_{x\to2^+}f(x)=\lim_{x\to2}5x-10=0

For f to be continuous at x=2, then, we'd need to have

4a+2b=0

(iv) Taking both requirements from parts (ii) and (iii), we solve for a,b:

\begin{cases}a+b=2\\4a+2b=0\end{cases}\implies a=-2,b=4

I've attached a plot that confirms this is correct.

You might be interested in
Two groups of friends go to a movie. Each ticket costs the same amount. One group spends ​$57. The other group spends ​$95. List
kenny6666 [7]

Answer:

1) All possible number tickets for group that spends $57: A, B, C, D

2) All possible number tickets for group that spends $95: B, C, E, F

3) Each ticket will cost at most $19

Step-by-step explanation:

We are told that one group spends $57 dollars while the other group spends $95.

Now,we want to find all possible whole number ticket prices for each group and at most how much each ticket​ costs.

To do this, let's first find the factors of both amounts which will give us all possible whole number ticket prices for each group.

57: 1, 3, 19, 57

95: 1, 5, 19, 95

Since each ticket costs same amount, to find out at most how much each ticket costs, we will select the highest common factor of both groups which is 19.

Thus,each ticket will cost at most $19

8 0
3 years ago
Plz help me with this
erica [24]

Answer:

the answer is b

Step-by-step explanation:

b is 9 thank you

3 0
3 years ago
Read 2 more answers
A pair of shoes is on sale for 15% off. With this discount, customers will save $9 if they buy the shoes. Part AIn this situatio
In-s [12.5K]

Answer:

(b)The original price of the shoes is $60.

Explanation:

Part A

In this situation:

• 15% is the PERCENT

,

• $9 is the PART

,

• The original price is the WHOLE.

Part B

If 15% is taken off, the customer will save $9.

This means that 15% of the original price = $9.

Let the original price=p

\begin{gathered} 15\%\text{ of p=9} \\ \frac{15}{100}p=9 \\ 15p=900 \\ p=\frac{900}{15} \\ p=60 \end{gathered}

The original price of the shoes is $60.

8 0
1 year ago
Find the value of x.
Ira Lisetskai [31]

Answer:

The value of x is 0

Step-by-step explanation:

5 0
3 years ago
Perform the indicated operation. 10 3/7 + 19 5/9
DanielleElmas [232]
Given expression is

10 \frac{3}{7} + 19 \frac{5}{9}

Now convert mixed fraction as improper fraction as

10 \frac{3}{7} + 19 \frac{5}{9} =  \frac{10*7 + 3}{7} +  \frac{19*9+5}{9}
                                                         =  \frac{73}{7}  +  \frac{176}{9}
                                                          =  \frac{73*9 + 176 * 7}{63}
                                                         =  \frac{657 + 1232}{63} =  \frac{1889}{63}
Now we can convert \frac{1889}{63 } = 29 \frac{62}{63}

So the answer is 29 \frac{62}63}
4 0
3 years ago
Read 2 more answers
Other questions:
  • A rectangular prism has a base with an area of 200 cm. The volume of the prism is 3,000 cm. What id the height of the prism?
    14·1 answer
  • Geometry<br> An angle is formed by:
    7·2 answers
  • The radius of a cylindrical water tank is 5.5ft, and its height is 8ft
    7·1 answer
  • Find the point slope equation fir the line that passes through the points (-6,24)(5,-31)
    10·1 answer
  • 1. A bag of apples at HEB costs $2.49 for 6 apples. What is the price per apple.
    8·2 answers
  • Find the missing exponent: p^2 ∙ p^3 ∙p^? = p^9
    15·1 answer
  • Given an example of a binomial and an example of a trinomial.
    12·1 answer
  • Need help with #16 please
    12·1 answer
  • Jesse has four friends over to study. He bakes four pizzas to share equally for lunch. His father takes half of one when the piz
    9·1 answer
  • Someone please help me
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!