Tutoring calculus, you cover limits. The tutor mentions using Excel for confirmation. Because of Excel’s power, it can do some particular calculations you might use to verify a calculus limit. Example: In my April 19, 2016 post I develop the…

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Tutoring calculus, you cover limits. The tutor mentions using Excel for confirmation. Because of Excel’s power, it can do some particular calculations you might use to verify a calculus limit. Example: In my April 19, 2016 post I develop the…

Tutoring calculus or differential equations, Newton’s Law of Cooling will surface. The tutor looks at a real-life example. In yesterday’s post I mention that a casserole dish taken out of the oven cooled from 177C to about 40C during one…

Tagged with: finding the constant in Newton's law of cooling

Tutoring math, you encounter the differences between calculators even from the same manufacturer. Now, the tutor shows how to convert from rectangular to polar coordinates using the Casio fx-991ES PLUS C. In my post from May 18 I show how…

Tutoring calculus, you cover polar coordinates. The tutor shows how to convert from rectangular to polar coordinates on the Casio fx-260solar. Example: Convert the coordinates (-56,12) to polar with the Casio fx-260solar. Solution: Key in 56 +/- SHIFT + 12…

The tutor uses l’Hôpital’s rule to find a limit of form ∞/∞. l’Hôpital’s rule states that the limit of a quotient of form ∞/∞ or 0/0 can be found as follows: lim (f(x)/g(x)) = lim (f'(x)/g'(x)) In this case [noting…

The tutor shows the derivative of arcsin, the inverse of sin. In yesterday’s post I explained the formula for the derivative of an inverse function (m-1(x))’ = 1/m'(m-1(x)) Today, I’ll use it to find the derivative of “inverse sin(x)”, aka…

The tutor shows the development of a formula for the derivative of an inverse. Let’s imagine m(x) is a function with inverse m-1(x). Then m(m-1(x)) = x By implicit differentiation, [m(m-1(x))]’ = 1 By the chain rule, [m(m-1(x))]’ = m'(m-1(x))*(m-1(x))’…

The tutor shows the example ∫dx/(x2+6) ∫dx/(x2+1) = arctanx + C The related integral ∫dx/(x2+6) must be put in the form, as follows: ∫dx/(x2+6) = ∫dx/(6(x2/6+1)) = 1/6 ∫dx/(x2/6 + 1) =1/6 ∫dx/((x/√6)2+1) = (√6)/6∫(dx(1/√6))/((x/√6)2 + 1) Next it becomes…

Tagged with: arctan integral

The tutor looks at forming a Taylor polynomial with the example of square root 31. A transcendental function is one there is no operation for. Rather, it’s represented by a series of expressions. Square root and sin are two examples.…

Tagged with: transcendental function

The tutor explains concavity and point of inflection with an example. Concavity refers to an aspect of graph shape. My first-year calculus professor explained it this way: concave upward will collect rain, while concave downward will shed rain. Numerically, when…

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