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
zimovet [89]
2 years ago
11

PRECAL: Having trouble on this review, need some help.

Mathematics
1 answer:
ra1l [238]2 years ago
6 0

1. As you can tell from the function definition and plot, there's a discontinuity at x = -2. But in the limit from either side of x = -2, f(x) is approaching the value at the empty circle:

\displaystyle \lim_{x\to-2}f(x) = \lim_{x\to-2}(x-2) = -2-2 = \boxed{-4}

Basically, since x is approaching -2, we are talking about values of x such x ≠ 2. Then we can compute the limit by taking the expression from the definition of f(x) using that x ≠ 2.

2. f(x) is continuous at x = -1, so the limit can be computed directly again:

\displaystyle \lim_{x\to-1} f(x) = \lim_{x\to-1}(x-2) = -1-2=\boxed{-3}

3. Using the same reasoning as in (1), the limit would be the value of f(x) at the empty circle in the graph. So

\displaystyle \lim_{x\to-2}f(x) = \boxed{-1}

4. Your answer is correct; the limit doesn't exist because there is a jump discontinuity. f(x) approaches two different values depending on which direction x is approaching 2.

5. It's a bit difficult to see, but it looks like x is approaching 2 from above/from the right, in which case

\displaystyle \lim_{x\to2^+}f(x) = \boxed{0}

When x approaches 2 from above, we assume x > 2. And according to the plot, we have f(x) = 0 whenever x > 2.

6. It should be rather clear from the plot that

\displaystyle \lim_{x\to0}f(x) = \lim_{x\to0}(\sin(x)+3) = \sin(0) + 3 = \boxed{3}

because sin(x) + 3 is continuous at x = 0. On the other hand, the limit at infinity doesn't exist because sin(x) oscillates between -1 and 1 forever, never landing on a single finite value.

For 7-8, divide through each term by the largest power of x in the expression:

7. Divide through by x². Every remaining rational term will converge to 0.

\displaystyle \lim_{x\to\infty}\frac{x^2+x-12}{2x^2-5x-3} = \lim_{x\to\infty}\frac{1+\frac1x-\frac{12}{x^2}}{2-\frac5x-\frac3{x^2}}=\boxed{\frac12}

8. Divide through by x² again:

\displaystyle \lim_{x\to-\infty}\frac{x+3}{x^2+x-12} = \lim_{x\to-\infty}\frac{\frac1x+\frac3{x^2}}{1+\frac1x-\frac{12}{x^2}} = \frac01 = \boxed{0}

9. Factorize the numerator and denominator. Then bearing in mind that "x is approaching 6" means x ≠ 6, we can cancel a factor of x - 6:

\displaystyle \lim_{x\to6}\frac{2x^2-12x}{x^2-4x-12}=\lim_{x\to6}\frac{2x(x-6)}{(x+2)(x-6)} = \lim_{x\to6}\frac{2x}{x+2} = \frac{2\times6}{6+2}=\boxed{\frac32}

10. Factorize the numerator and simplify:

\dfrac{-2x^2+2}{x+1} = -2 \times \dfrac{x^2-1}{x+1} = -2 \times \dfrac{(x+1)(x-1)}{x+1} = -2(x-1) = -2x+2

where the last equality holds because x is approaching +∞, so we can assume x ≠ -1. Then the limit is

\displaystyle \lim_{x\to\infty} \frac{-2x^2+2}{x+1} = \lim_{x\to\infty} (-2x+2) = \boxed{-\infty}

You might be interested in
So, here’s a math question for you: Suppose you set your confidence level at "I think I know it," which means that you’re initia
stiks02 [169]

Answer:

The answer is 20 points

Step-by-step explanation:

If the points is based on 100 by rating, and your confidence level of 'I think I know it' places you on the initial risk of 80 points as suggested, which eventually places you on the wrong side, you will be left with the following:

Total rating point of 100 minus initial risking points of 80. This leaves you with a second chance points of just 20.

6 0
3 years ago
What values of c and d makes the equation true?​
den301095 [7]

Answer:

c 6 d 4 I hope it will help you please follow me

4 0
3 years ago
Please help me I I will give you a Brainly
Dimas [21]

Step-by-step explanation:

by deleting

9y = -9

y = -1

6x - 4 = -10

6x = -6 then x = -1

5 0
3 years ago
1. r - 29 = -2r + 19
Sphinxa [80]

Answer: r=16

Step-by-step explanation:

r-29=-2r+19

r=−2r+19+29

r=−2r+48

r+2r=48

3r=48

r=48/3

r=16

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)  

- Cutiepatutie ☺❀❤

7 0
3 years ago
Someone please I’m begging this is due by midnight and I can’t have it be late
Thepotemich [5.8K]

Answer:

(1) Coeficcient (2) Constant (3) 4 terms (4) In descending order, 2, 1, 3, 4 (5) -2 (6) 1 (7) 5 (8) 2 (9) -15, 5x, -7x^2, 2x^3 (10) -4x^2y, 2xy, 5x, 7

Step-by-step explanation:

Sorry if I got one wrong

8 0
3 years ago
Read 2 more answers
Other questions:
  • What is five times five?
    15·2 answers
  • can u guys take some time and help me on my math in my profile please can we talk i need someone to help me brainly teacher anyo
    9·1 answer
  • 2.2. A vine called the mile-a-minute weed is known for growing at a very fast rate. It can grow up to 0.5 ft per day. How fast i
    11·2 answers
  • The time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean va
    15·1 answer
  • What is the phase shift of y = –csc(3x − π)?
    7·2 answers
  • A teacher needs 70 lengths of string cut to 40cm each. If balls of string are 10 m long, how many balls will be needed.
    7·1 answer
  • Please help!!!! I'll give brainliest!<br><br> Image of question is attached.
    7·2 answers
  • What ratio is not equivalent to 5:8
    8·1 answer
  • 75 - { ( 8 x 3 ) + 6 }
    6·2 answers
  • Find three points on the parabola.<br> x^2−6x−4y+5=0
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!