Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/25



For the convenience of the student we give the following list of elementary formulas from Algebra, Geometry, Trigonometry, and Analytic Geometry. Binomial Theorem ($$\scriptscriptstyle{n}$$ being a positive integer):

$$\scriptstyle{n!=\begin{array}{|c}\scriptscriptstyle{n}\\\hline\end{array}=1\cdot2\cdot3\cdot4\cdots(n-1)n.}$$

In the quadratic equation $$\scriptstyle{ax^2+bx+c=0}$$,

When a quadratic equation is reduced to the form $$\scriptstyle{x^2+px+q=0}$$,

In an arithmetical series,

In a geometrical series,

$$\scriptstyle{\log ab=\log a+\log b}$$.

$$\scriptstyle{\log\frac{a}{b}=\log a-\log b}$$.

$$\scriptstyle{\log a^n=n\log a}$$.

$$\scriptstyle{\log\sqrt[n]{a}=\frac{1}{n}\log a}$$.

$$\scriptstyle{\log 1=0}$$.

$$\scriptstyle{\log_a a=1}$$.

$$\scriptstyle{\log\frac{1}{a}=-\log a}$$.

Circumference of circle$$\scriptstyle{=2\pi r}$$.

Area of circle$$\scriptstyle{=\pi r^2}$$.