Video links for STAT students.

Dear class, Not all YouTube math videos are created equal!! I will post links to the most useful ones here:   Confidence Intervals: Introduction to confidence intervals When sigma is known When sigma is unknown   Central Limit Theorem: Main idea. Another Example.   If you want me to post more post a comment about […]

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Answers to homework.

1. Find an equation of the tangent to the curve that is parallel to x−4y = 1. (It is better to leave the natural log in the equation, don't find a decimal value... Though you may use such value for graphing.) 2. Find an equation of the tangent to the curve that will pass through […]

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Counting using products.

Today I proved the binomial theorem for my class. I did an informal proof showing them how, if we consider the set containing the alphabet: and the following product. expanding this produces a sum with every combination of the letter a-z: if we count all of the terms in this sum with, say three elements, […]

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Looks can be deceiving!

Look at the graph in the previous post. I was right! They don't intersect at a common point, rather the limit of the consecutive intersections is . This is just numeric, from Mathematica ... I'll try to prove it later... By the way an answer to the question of fining a curve orthogonal to the […]

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Quickie.

A curve A is orthogonal to B is the tangent lines at their intersections are perpendicular. Thinking of the follium of Descartes again, give the equation for a function orthogonal to the follium. I have found one trivial answer that requires no complex calculations. (Do, you see it?) On the other hand, it's quite hard […]

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Fixed points.

"Prove that if f,g are continuous functions on [0,1] with range [0,1], then there exists a point c such the " This is a variation on a popular problem given to encourage students to use the intermediate value theorem. The proof involves a function , this function can't be exclusively positive or negative, so we […]

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Rational points on the folium.

My students are studying implicit differentiation, we look at the folium of Descartes: They found the equation of the tangent at For their homework I want to have them look at another point, but I wanted it to be rational, I almost gave them the origin... But that's good. The expression given by implicit differentiation […]

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