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 …
Calculus: derivative of an inverse: derivative of arcsin Read more »
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 »
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 …
The tutor shows how to remind yourself that the derivative of tanx is sec2x. Let’s imagine you don’t recall that (tanx)’=sec2x. Here’s how to reconstruct it: Recall that tanx=sinx/cosx Take the derivative of sinx/cosx using the quotient rule:(u/v)’ = (vu’-uv’)/v2 …
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The tutor explores how to detect and solve exact differential equations with a very simple example. When a differential equation of the form P(x,y) +Q(x,y)y’ = 0 results from the implicit differentiation of an original equation F(x,y)=c, the equation P(x,y) …
Differential equations: exact differential equation Read more »
The tutor explains the idea of odd function vs even function. An odd function is one that gives the opposite output for -x as for x: f(x) odd, then f(-x) = -f(x) x3 and sinx are both odd functions: (-2)3=-8, …
Math: what is an odd function? What is an even function? Read more »