Evaluate the limit as theta approaches 0. (cos θ tan θ) / θ

1 answer:

5 0

We are given with the expression (cos θ tan θ) / θ and asked to evaluate the expression to limit as theta approaches zero. In this case, we substitute first zero. The answer is zero over zero. This is indeterminate so we derive the terms accdg to L'hopital's rule. The derivative is cos θ* sec^2 θ - sin θ tan θ /1. cos θ is 1 so is sec θ. Hence the answer is 1.

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Veronika [31]

Answer:

99% of the sample means will fall between 0.93288 and 0.94112.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, 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 normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .