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pshichka [43]
3 years ago
12

Compute the limit of the following as x approaches infinity.

Mathematics
1 answer:
Nonamiya [84]3 years ago
3 0

Yes, that's the correct limit.

\sqrt{x^2+1}-x=\dfrac1{\sqrt{x^2+1}+x}=\dfrac1{\sqrt{x^2}\sqrt{1+\frac1{x^2}}+x}

\sqrt{x^2}=|x|, but since x\to\infty, we are considering x>0, for which |x|=x. Then

\displaystyle\lim_{x\to\infty}\sqrt{x^2+1}-x=\lim_{x\to\infty}\frac1{x\left(\sqrt{1+\frac1{x^2}}+1\right)}

and both \dfrac1x and \dfrac1{x^2} vanish as x\to\infty, making the overall limit 0.

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Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
Svet_ta [14]

Answer:

I, II and III

Step-by-step explanation:

Two sides of a triangle have length 6 and 8.

the maximum possible area occurs in the right angle .

To find maximum area we use the area of the triangle formula

area of triangle = \frac{6 \cdot 8}{2} = 24

So maximum possible area is 24 units^2

all the given possible values are less than and equal to 24

so all the three options are correct

I, II and III

4 0
3 years ago
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Solnce55 [7]
Red to total I believe is 12/23
4 0
3 years ago
Which statements are true for the following expression?<br> (9 + 1) · 5
kvasek [131]

Answer:

50

Step-by-step explanation:

add

9 + 1 = 10

multiply

10 * 5 = 50

Answer: 50

3 0
2 years ago
Write the pair of fractions as a pair of fractions with a common denominator |
trapecia [35]

Answer:

3/10 and 2/5 = 3/10 and 4/10

1/3 and 3/4 = 4/12 and 9/12

Step-by-step explanation:

For 3/10 and 2/5

* Find the lcm (least common multiple) of the denominators which are 10 and  

 5. The multiples of 10 are: 10, 20, 30 etc and the multiples of 5 are: 5, 10 15,

 etc. So, the lcm is 10. It is the smallest multiple that the denomitaotrs share.

* Next multiply the numerators (3 and 2) by whatever number you use to

  multiply the denominator by to get 10. For 3/10, the denominator stayed the

  same, so to get 10, you need to multiply 10 by 1. Do the same for the

  numerator. 3 x 1 = 3. So, the first factor pair is 3/10.

* The second factor pair is 2/5, so we are still using the lcm of 10. So, what

  do you need to multiply 5 by to get 10? The answer is 2. Now just multiply

  the numerator (2) by 2 and you get 4. The second factor pair is now 4/10.

5 0
3 years ago
Estimate the unit rate to the nearest hundredth $2.35 12 Grade AA eggs.<br>​
Wewaii [24]

Answer:

2.4

Step-by-step explanation:

6 0
3 years ago
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