Comments for MathPhys Archive
http://sunglee.us/mathphysarchive
The archive of my lecture notes on mathematics, physics and other related subjects.Mon, 05 Nov 2018 11:33:49 +0000hourly1https://wordpress.org/?v=4.9.6Comment on L’Hôpital’s Rule by Sequences | MathPhys Archive
http://sunglee.us/mathphysarchive/?p=3089#comment-498917
Mon, 05 Nov 2018 11:33:49 +0000http://sunglee.us/mathphysarchive/?p=3089#comment-498917[…] The following theorem enables you to use a cool formula you learned in Calculus I, L’Hôpital’s rule! […]
]]>Comment on Integration by Parts by Trigonometric Integrals | MathPhys Archive
http://sunglee.us/mathphysarchive/?p=2082#comment-498738
Wed, 24 Oct 2018 21:34:30 +0000http://sunglee.us/mathphysarchive/?p=2082#comment-498738[…] -(n-1)cos^{n-2}xsin x & stackrel{-}{longrightarrow} & sin x\ end{array}$$ By integration by parts, we have begin{align*} intcos^n xdx&=cos^{n-1}xsin x+(n-1)intcos^{n-2}xsin^2xdx\ […]
]]>Comment on Approximating Functions with Polynomials by Taylor series | MathPhys Archive
http://sunglee.us/mathphysarchive/?p=2894#comment-498614
Sun, 21 Oct 2018 23:40:57 +0000http://sunglee.us/mathphysarchive/?p=2894#comment-498614[…] following theorem tells when a function $f(x)$ can be represented by its Taylor series. Recall that $f(x)=T_n(x)+R_n(x)$ where $T_n(x)$ is the $n$-th degree Taylor polynomial of $f$ at $a$ and […]
]]>Comment on Alternating Series, Absolute and Conditional Convergence by Properties of Power Series | MathPhys Archive
http://sunglee.us/mathphysarchive/?p=2850#comment-498264
Wed, 17 Oct 2018 02:42:39 +0000http://sunglee.us/mathphysarchive/?p=2850#comment-498264[…] becomes $sum_{n=1}^inftyfrac{(-1)^n}{n}$. This is an alternating harmonic series and we learned here that it converges. If $x=4$, the series becomes the harmonic series $sum_{n=1}^inftyfrac{1}{n}$ […]
]]>Comment on Mean Value Theorem by Approximating Functions with Polynomials | MathPhys Archive
http://sunglee.us/mathphysarchive/?p=2044#comment-497465
Tue, 09 Oct 2018 16:08:24 +0000http://sunglee.us/mathphysarchive/?p=2044#comment-497465[…] Recall the Mean Value Theorem: If $f(x)$ is continuous on $[a,x]$ and is differentiable on $(a,x)$, then there exists […]
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