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svetoff [14.1K]
3 years ago
15

Evaluate the limit, if it exists. (if an answer does not exist, enter dne.) lim h→0 (5 + h)−1 − 5−1 h

Mathematics
1 answer:
34kurt3 years ago
4 0
\displaystyle\lim_{h\to0}\frac{(5+h)^{-1}-5^{-1}}h=\lim_{h\to0}\frac{\frac5{5(5+h)}-\frac{5+h}{5(5+h)}}h
\displaystyle=-\lim_{h\to0}\frac h{5(5+h)h}
\displaystyle=-\lim_{h\to0}\frac1{5(5+h)}=-\frac1{25}

Alternatively, recall that if f(x)=\dfrac1x, then f'(x)=-\dfrac1{x^2}, and so

f'(5)=\displaystyle\lim_{x\to5}\frac{\frac1x-\frac15}{x-5}

Take h=x-5, so that x=h+5, and we have the original limit. So the limit is equivalent to the value of f'(5), i.e.

f'(5)=-\dfrac1{5^2}=-\dfrac1{25}
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2 years ago
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Simplify this expression: -2(-4x + 2y - 6)
Monica [59]

Answer:

8x - 4y + 12

Step-by-step explanation:

-2(-4x + 2y - 6)

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2 years ago
The jug can hold 1500ml. The bucket can hold 2 litres. The barrel can hold 15 litres. Anisa wants to fill the barrel with water.
myrzilka [38]

Answer:

1. Using the jug 6 times and the bucket 3 times

2. Using the bucket 6 times, then using the jug two times

Step-by-step explanation:

Firstly, let’s remember that 1000 ml = 1l

Thus 2L = 2000 ml

And 15L = 15,000 ml

So the situation we are having now is that we want to fill a barrel of 15,000 ml using a jug of 1500 ml and a bucket with a capacity of 2000 ml

Firstly, the first way is using the bucket 6 times and the jug 2 times

What i mean by this is using the bucket 6 times bringing the total volume from the bucket as (6* 2000) = 12,000 ml

Then we are left with 15,000-12,000 = 3,000 ml

Now, she can fill the barrel with 2 times the full volume of the jug making 3,000

Secondly, she can also use the combination of both.

She can use the bucket 6 times and the jug 2 times

The total volume in each case here would be;

For the bucket; (2,000 * 6) = 12,000 ml

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And thus we shall be having a total of 12,000 + 3,000 = 15,000 ml this way

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Answer:

25.2 weeks until everyone on the planet is infected

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