Tutoring calculus, trig identities can give choices when performing derivatives. The tutor mentions an example. Example: find derivative of y=sinxcosx Solution method 1: product rule (see my post here.) y’ = (sinx)’cosx + sinx(cosx)’ = cosxcosx – sinxsinx = (cosx)^2 …
Calculus: trig derivative: product rule or identity substitution? Read more »
Tutoring calculus, the idea of a limit is important. The tutor mentions some thoughts. A limit, in calculus, is important, because it opens the door to certain functions, procedures, and assumptions. Numerous mechanisms are available to prove or disprove the …
Tutoring calculus, average values come up. The tutor mentions an example. In calculus, the average value of a function f(x) over a given interval (a,b) is sometimes defined as ∫abf(x)/(b-a). That is, it’s the integral of the function over that …
Tutoring calculus, series convergence comes up. The tutor mentions the limit ratio test for convergence of an infinite series. Put concisely, the limit ratio test looks at the following: limn->∞|tn+1 ÷ tn|. If the limit < 1, then the series …
Tutoring calculus, infinite series come up. The tutor mentions one way to realize the convergence of the infinite series 1/n^2. The series 1/n^2, meaning 1/1 + 1/4 + 1/9 + 1/16 + 1/25 + …. converges; even though it has …
Calculus: why the infinite series 1/n^2, n ε N, converges Read more »
Tutoring calculus, everyday formulas students count on can often be verified. The tutor mentions the derivative of tanx. It’s true that (tanx)’ = (secx)^2. But why? Realizing tanx = sinx/cosx, then using the the quotient rule (u/v)’ = (vu’ – …
Calculus: why the derivative of tanx is (secx)^2 Read more »
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 …
Calculus: transcendental functions and derivatives Read more »
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 …
Calculus: using Excel to verify limit nth root of n, n goes to infinity Read more »
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 …