From 6a1257b0c8afc799f32f9a23ca6346c8c089e0d9 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Sun, 26 Aug 2018 18:40:07 +1000 Subject: [PATCH] refinements to calculus notes --- spec/calculus.md | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/spec/calculus.md b/spec/calculus.md index f98aee7..08cfe8f 100644 --- a/spec/calculus.md +++ b/spec/calculus.md @@ -144,6 +144,7 @@ $\log_b y^{x^n} = x^n \log_b y$ $b^{m+n}=b^m \cdot b^n$ $(b^m)^n=b^{m \cdot n}$ $(b \cdot c)^n = b^n \cdot c^n$ +${a^m \div a^n} = {a^{m-n}}$ ### $e$ as a logarithm @@ -182,7 +183,7 @@ $$\int f(x) dx = F(x) + c$$ - area enclosed by curves - $+c$ should be shown on each step without $\int$ -$$\int xn = {x^{n+1} \over n+1} + c$$ +$$\int x^n = {x^{n+1} \over n+1} + c$$ ### Integral laws @@ -191,10 +192,11 @@ $\int k f(x) dx = k \int f(x) dx$ | $f(x)$ | $\int f(x) \cdot dx$ | | ------------------------------- | ---------------------------- | -| $k$ (constant) | $kc + c$ | +| $k$ (constant) | $kx + c$ | | $x^n$ | ${1 \over {n+1}}x^{n+1} + c$ | -| $1 \over x$ | $\log_e x + c$ | -| $e^kx$ | ${1 \over k} e^{kx} + c$ | +| $a \cdot {1 \over x}$ | $a \cdot \log_e x + c$ | +| $e^{kx}$ | ${1 \over k} e^{kx} + c$ | +| $e^k$ | $e^kx + c$ | | $\sin kx$ | $-{1 \over k} \cos (kx) + c$ | | $\cos kx$ | ${1 \over k} \sin (kx) + c$ | | ${f^\prime (x)} \over {f(x)}$ | $\log_e f(x) + c$ | -- 2.43.2