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kkurt [141]
3 years ago
7

Which set of numbers is INFINITE?

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
7 0
Im pe\retty sure its D because they can be multiplied byt he sam enumber many tines

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PRECAL:<br> Having trouble on this review, need some help.
ra1l [238]

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}

6 0
2 years ago
Which expression is equivalent to -11 - (-7)?
snow_lady [41]

Answer:

d

Step-by-step explanation:

=-4

5 0
3 years ago
Read 2 more answers
PLEASE HELP!<br><br>write an expression ( simplified ) for the perimeter of the given figure ​
liraira [26]

Answer:

Step-by-step explanation:

2(3x-1)+2(6)

6x-2+12

6x+10

8 0
3 years ago
Read 2 more answers
Square numbers less than 40​
Citrus2011 [14]

Answer:

1 =1 X 1

2 4 =2 X 2

3 9 =3 X 3

4 16 =4 X 4

5 25 =5 X 5

6 36 =6 X 6

7 49 =7 X 7

8 64 =8 X 8

9 81 =9 X 9

10 100 =10 X 10

11 121 =11 X 11

12 144 =12 X 12

13 169 =13 X 13

14 196 =14 X 14

15 225 =15 X 15

16 256 =16 X 16

17 289 =17 X 17

18 324 =18 X 18

19 361 =19 X 19

20 400 =20 X 20

21 441 =21 X 21

22 484 =22 X 22

23 529 =23 X 23

24 576 =24 X 24

25 625 =25 X 25

26 676 =26 X 26

27 729 =27 X 27

28 784 =28 X 28

29 841 =29 X 29

30 900 =30 X 30

31 961 =31 X 31

32 1024 =32 X 32

33 1089 =33 X 33

34 1156 =34 X 34

35 1225 =35 X 35

36 1296 =36 X 36

37 1369 =37 X 37

38 1444 =38 X 38

39 1521 =39 X 39

40 1600 =40 X 40

6 0
2 years ago
If old reeses cost $6 for a 12 pack and new reeses cost $1/pack, by what percent did the cost of reeses increase?s
skad [1K]

Answer:

Step-by-step explanation:

6 dollars for a 12 pack means that it was $0.50 each. now they cost a dollar per pack. it's a 50 cent increase, or a 100% percentage increase

8 0
3 years ago
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