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never [62]
3 years ago
15

Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim x→8 1 + 3 x 5 − 6x2 + x3

Mathematics
1 answer:
Sergio [31]3 years ago
5 0

Answer:

[tex] lim_{x \to 8} (1+3\sqrt{x})(1-6x^2 +x^3)=1-384 +512+3\sqrt{8} -18(8)^{5/2} +3 (8)^{7/2} =1223.601

And the limit on this case exists.

Step-by-step explanation:

We want to find the following limit:

lim_{x \to 8} (1+3\sqrt{x})(1-6x^2 +x^3)

First we can distribute the polynomials like this:

lim_{x \to 8} (1-6x^2 +x^3+3\sqrt{x} -18 x^{5/2} +3x^{7/2})

And Now we can use the distributive property for the limit and we got:

lim_{x \to 8} 1 - 6 lim_{x \to 8} x^2 + lim_{x \to 8} x^3 +3 lim_{x \to 8} \sqrt{x} -18 lim_{x \to 8} x^{5/2} + 3 lim_{x \to 8} x^{7/2}

And now we can evaluate the limit and we got:

[tex] lim_{x \to 8} (1+3\sqrt{x})(1-6x^2 +x^3)=1-384 +512+3\sqrt{8} -18(8)^{5/2} +3 (8)^{7/2} =1223.601

And the limit on this case exists.

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Maria decides to increase her homework time of 8 hours per week by 15% Calculate her new homework time. Give your answer in hour
Elena-2011 [213]

Answer:

Maria's homework time is now 9 hours 12 minutes.

Step-by-step explanation:

Since Maria decides to increase her homework time by 15%.

Then,

15% of 8 hours = \frac{15}{100} x 8 hours

                        = 0.15 x 8 hours

                        = 1.2 hours

(Note that: 1.2 hours = 1 hour 12 minutes)

15% of 8 hours = 1 hour 12 minutes

her new homework time = 8 hours + 1 hour 12 minutes

                              = 9 hours 12 minutes

Maria's homework time is now 9 hours 12 minutes.

8 0
3 years ago
A pound of coffee beans yields 60 cups of coffee (4 cups = 1 qt). how many milliliters of coffee can be obtained from 1.0 g of c
kari74 [83]
We can easily convert grams to pounds and find that 1 g of coffee beans is 0.00220462 pounds. Now we can multiply that value with 60 cups to find how many cups it makes.

We find that it makes 0.1322772 cups.

Then we know that 236.588 milliliters are in a cup. We multiply the value of the coffee available with 1 g of coffee beans (in cups - of course) and get the value the question asked :

0.1322772 * 236.588 milliliters

The answer is 31.2951981936 milliliters!

Hope this helps!

5 0
3 years ago
LEIM deposits some money in an account which pays 5% simple interest per year, and twice that amount in an account paying 4% sim
Tamiku [17]

Answer:

266.5

Step-by-step explanation:

$533.00* 5%=266.5

8 0
3 years ago
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Ivahew [28]

Answer:

A 3 x 4 x 8 inch triangle

Step-by-step explanation:

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Step-by-step explanation:

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