Category: calculus

Calculus: using Excel to verify limit nth root of n, n goes to infinity

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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Calculus: the cooling constant of the casserole

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

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Calculator usage: converting from rectangular to polar coordinates using the Casio fx-991ES PLUS C

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

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Calculator usage: how to convert rectangular coordinates to polar with the Casio fx-260solar

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

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Calculus: l’Hôpital’s rule: lim(x→∞) lnx/square root x

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

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Calculus: derivative of an inverse: derivative of arcsin

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

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Calculus: the derivative of an inverse function

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))’

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Calculus: an arctan integral

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

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Math: evaluating transcendental functions: Taylor polynomial for square root

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.

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Calculus: concavity and point of inflection

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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