Tutoring calculus, transcendental functions are important. The tutor mentions some examples of derivatives with them. Transcendental functions are ones that can’t be written in polynomial form. Some examples: sinx, logx, ex. Importantly, their derivates don’t collapse the way those of …
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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 …
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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 …
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 …
Calculus: l’Hôpital’s rule: lim(x→∞) lnx/square root x Read more →
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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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 …
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. …
Math: evaluating transcendental functions: Taylor polynomial for square root Read more →