Some of these theorems are the mean value theorem, the extreme value theorem, the intermediate value theorem, Rolle's theorem, and so on. Without proof that these statements concerning continuous functions are indeed true, calculus would not have the sturdy foundations that it does....
What is The Mean Value Theorem?(4) 中学数学教学教学方法函数正~~梁宇学中学生数学
What would be some functions where the mean value theorem does not hold and why would it not hold for those functions?What does the extreme value theorem say?Use the Mean Value Theorem to prove sin^2(3 x) + cos^2(3 x) = 1Show that |cos x-1| leq |x| for all x by using the...
This rounding error is the characteristic feature of floating-point computation. The section Relative Error and Ulps describes how it is measured. Since most floating-point calculations have rounding error anyway, does it matter if the basic arithmetic operations introduce a little bit more rounding ...
Prove that if the functions g:[a,b] --> R and h:[a,b] --> R are continuous, with h(x)\geq0 for all x in [a,b] then there is a point c in (a,b) such that...
In order to find the SPSS mean mode median, you’ll need to use theFrequency table. It seems a little counter-intuitive, but the Descriptive Statistics tab does not give you the option to find the mode or the median. SPSS has a very similar interface to Microsoft Excel. Therefore, if ...
In the lesson on the Mean Value Theorem we thought about a race between two boats. The boats covered the same distance in the same amount of time, and so we concluded they must have been going the same speed sometime during the race. Let's take that same situation and adjust it slig...
Unfortunately, outliers and extreme values in the long tail of a skewed distribution can cause some sample statistics to become biased, poor quality estimates. What does that mean? The sample statistics will be systematically too high or too low and move further away from the correct value. ...
I don't think that there is any good engineer or scientist that can get along on an IQ of 100, which is the average for human beings.In other words, he has to have an IQ higher than that. Everyone in this room is considerably above that. This, we might say, is a matter of envi...
I went back several courses to refresh what I've learned in the past and I already know more now than I ever did taking the course online. Jen does an amazing job of explaining the material, giving the formulas, and showing where the formulas come from so that you don't HAVE to ...