All categories

3 years ago

HELP Use the definition of continuity and the properties of limits to show that’s the function…

Mathematics

1 answer:

Solnce55 [7]3 years ago

4 0

Answer with Step-by-step explanation:

We are given that

$g(x)=(x^2-3x-10)(x^2+2x^2-5x+4)$

x=-1

Using property of limit

$\lim_{x\rightarrow -1}g(x)=\lim_{x\rightarrow -1}(x^2-3x-10)(3x^2-5x+4)$

= $(1+3-10)(3+5+4)$

= $(-6)(12)$

= $-72$

$g(-1)=(1+3-10)(1+2+5+4)$

$g(-1)=(-6)(12)=-72$

$\lim_{x\rightarrow -1}g(x)=g(-1)$

Hence, the function is continuous at x=-1

You might be interested in

In which number does the digit 2 have a value that is ten times as great as the value of the digit 2 in the number 135,284?

Valentin [98]

Answer: See explanation

Step-by-step explanation:

You didn't give the options but let me help out.

First and foremost, we should note that the value of the digit 2 in the number 135,284 is 200. Therefore, the value that is ten times as great as the value of the digit 2 in the number 135,284 would be:

= 10 × 200

= 2000

Therefore, the 2 must be in the thousands place. This can be seen in numbers such as:

172748.

6 0

3 years ago

A box of books has a mass of 4.10 kilogram for ever meter of its height a box of magazines has a mass of 3 pounds for every foot

Tju [1.3M]

No rounding is necessary to answer the question.

We can subtract the (linear) density of the second box from that of the first to see which box is heavier per unit height.

$\dfrac{4.10\,kg}{1\,m}-\dfrac{3\,lb}{1\,ft}=\dfrac{4.10\,kg}{1\,m}\cdot\dfrac{1\,lb}{0.45\,kg}-\dfrac{3\,lb}{1\,ft}\cdot\dfrac{3.28\,ft}{1\,m}\\\\=\dfrac{4.10\,lb}{0.45\,m}-\dfrac{3\cdot 3.28\,lb}{1\,m}=\dfrac{4.10-3\cdot 3.28\cdot 0.45}{0.45}\dfrac{lb}{m}=\dfrac{4.10-4.428}{0.45}\dfrac{lb}{m}$

This value is obviously less than zero, so ...

... the box of magazines has the greater mass per unit height.

_____

The question didn't ask for the mass per height, and we didn't compute it. All we did was make a conversion to comparable units. The units we ended up with are mixed English and metric units, but that doesn't matter for the purpose of comparison.

Since all we're really interested in is <em>the sign of the difference</em> of mass/height, we don't even need to actually compute that difference. We just need to do enough computation to be able to tell whether the sign is positive or negative.

3 0

4 years ago

Is the sequence 5,9,15 an arithmethic sequence explain ?

german

If a, b, c is an arithmetic sequence then a + c = 2b

a = 5, b = 9, c = 15

subtitute

a + c = 5 + 15 = 20

2b = 2 · 9 = 18

20 ≠ 18

Answer: The sequence 5, 9, 15 is not an arithmetic sequence.

8 0

3 years ago

PLEASE SOMEONE HELP MEE I NEED THIS BADLY

masya89 [10]

y = 6^x - 3

The graph goes through (0,-2) and (1,3)

3 0

3 years ago

A small town's raffle has 85 entries and 3 gift baskets that three different people could win. What is the probability of winnin

mr_godi [17]

Answer:

Step-by-step explanation:

This problem is on probabilty since there are a number of entries to be selected from which are 85 entries, the chances of winning one of the prices if selected is

the number of entries you have/ total number of entries

given that the total entry is 85

and that you have one entry

Since there are three gift baskets you have three chances to win one.

hence there will be a total of three draws, and after each draw, there won't be a replacement of the previous winner (as the winners are three distinct persons).

Hence the probability of winning a draw for the gift basket is

=1st draw+2nd draw+3rd draw

= 1/85+1/84+1/83

= 0.0117+0.0119+0.012

= 0.035

5 0

3 years ago