Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Concept explainers

Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
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Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…
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how do i solve? i asked this question before but was given the wrong answer of 1 which is not correct

The image presents a problem involving composed functions and their derivatives. Here is the transcription and explanation suitable for an educational website. --- ### Calculus Problem: Evaluating Composed Functions Consider the following table that provides values for functions \( f \) and \( g \), as well as their derivatives \( f' \) and \( g' \), at specific points: | \( x \) | \( f(x) \) | \( g(x) \) | \( f'(x) \) | \( g'(x) \) | |:------:|:-------:|:--------:|:--------:|:---------:| | 3 | 1 | 9 | 8 | 3 | | 4 | -3 | 3 | 2 | -5 | #### Problem: Calculate \( f(g(x)) \) for \( x = 4 \). Options: - (A) 24 - (B) -10 - (C) -40 - (D) 8 #### Solution: To find \( f(g(x)) \) when \( x = 4 \): 1. First, identify \( g(4) \) from the table, which is 3. 2. Next, find \( f(g(4)) \) which translates to \( f(3) \). 3. From the table, \( f(3) \) is given as 1. Therefore, \( f(g(4)) = f(3) = 1 \). None of the provided options (24, -10, -40, 8) match the correct answer, which is 1. It seems there may be a mistake in the options given. --- This transcription provides a step-by-step solution to the problem based on the given table.
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Transcribed Image Text:The image presents a problem involving composed functions and their derivatives. Here is the transcription and explanation suitable for an educational website. --- ### Calculus Problem: Evaluating Composed Functions Consider the following table that provides values for functions \( f \) and \( g \), as well as their derivatives \( f' \) and \( g' \), at specific points: | \( x \) | \( f(x) \) | \( g(x) \) | \( f'(x) \) | \( g'(x) \) | |:------:|:-------:|:--------:|:--------:|:---------:| | 3 | 1 | 9 | 8 | 3 | | 4 | -3 | 3 | 2 | -5 | #### Problem: Calculate \( f(g(x)) \) for \( x = 4 \). Options: - (A) 24 - (B) -10 - (C) -40 - (D) 8 #### Solution: To find \( f(g(x)) \) when \( x = 4 \): 1. First, identify \( g(4) \) from the table, which is 3. 2. Next, find \( f(g(4)) \) which translates to \( f(3) \). 3. From the table, \( f(3) \) is given as 1. Therefore, \( f(g(4)) = f(3) = 1 \). None of the provided options (24, -10, -40, 8) match the correct answer, which is 1. It seems there may be a mistake in the options given. --- This transcription provides a step-by-step solution to the problem based on the given table.
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