Question 2. (OpenStax Calculus, Volume 1, section 4.6, exercise 294) Find 3a3 -2 lim Question 3. I'm curious what range of values the function 2c+1 takes on over the interval (0, 00). Answer my curiosity in the following steps... Part A. Show that f (x) is always decreasing over (0, oo). Part B. Use limits and the fact that f(x) is continuous on (0, 00) (you don't have to prove continuity, although see Part D below) to find the largest and smallest values that f (x) takes on, or to show that there is no largest (and/or no smallest) value of f(x). Use those values to say what range of values f(x) takes on over the interval (0,00). Hint: what does the fact that f(x) is continuous and always decreasing tell you about where the largest and smallest values must occur? Part C. Use Mathematica or similar technology to graph f(x) over a large enough part of the interval (0, 0o) to visually check that your answer to Part B is plausible. Par t D. For up to 2 points of extra credit, prove that f(a) really is continuous on the interval (0, 00). Question 4. (Based on OpenStax Calculus, Volume 1, Problem 341 in Section 4.7.) Find the largest-volume right circular cylinder that fits inside a sphere of radius 1. Start by drawing a diagram of the situation
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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