Find the derivative of f(x)=7 by the limit process

1 answer:

6 0

$f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h$

If $f(x)=7$ , then

$f'(x)=\displaystyle\lim_{h\to0}\frac{7-7}h=0$

which is what you expect from a constant function.

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How Many Solutions? 3x - 7 = 3(x - 3) + 2 No Solution One Solution Infinite Solution

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Answer:

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Step-by-step explanation:

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Answer:

a) 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.

b) 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.

Step-by-step explanation:

To solve this question, it is important to know the Normal probability distribution and the Central Limit Theorem

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .