## Formulas and theorems in pure mathematics |

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Page 268

... as such by the laws of Algebra ; dl being written d„, and factors such as d.d,, in

which the independent variables are different, being written J,y, &c. EXPANSION

OF EXPLICIT FUNCTIONS.

... as such by the laws of Algebra ; dl being written d„, and factors such as d.d,, in

which the independent variables are different, being written J,y, &c. EXPANSION

OF EXPLICIT FUNCTIONS.

**TAYLOR'S THEOREM**.— EXPANSION OP f(x + h).Page 271

The theorem may be extended inductively to a function of three or more variables

. Thus, if u ... SYMBOLIC FORM OP

Theorem (150), writing the indices of d, as suffixes (1487), eM'/W = (1+W.+W* +.

The theorem may be extended inductively to a function of three or more variables

. Thus, if u ... SYMBOLIC FORM OP

**TAYLOR'S THEOREM**. ... By the ExponentialTheorem (150), writing the indices of d, as suffixes (1487), eM'/W = (1+W.+W* +.

Page 489

3288 *>u = a. Change from s to x by (1763) ; .'. — «;a«to = a, .'. s"8 = 2ax+c,

APPROXIMATE SOLUTION OF DIFFERENTIAL EQUATIONS BY

xyx+y, .

3288 *>u = a. Change from s to x by (1763) ; .'. — «;a«to = a, .'. s"8 = 2ax+c,

APPROXIMATE SOLUTION OF DIFFERENTIAL EQUATIONS BY

**TAYLOR'S****THEOREM**. 3289 The following example will illustrate the method : — Given yix =xyx+y, .

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### Contents

Introduction The C G S System of Units | 1 |

VHI Common and Hyperbolic Logarithms of | 7 |

QUANT1C8 1620 | 30 |

Copyright | |

108 other sections not shown

### Common terms and phrases

becomes Binomial Theorem bisect changes of sign chord circumscribing circle columns conic conjugate constant continued fraction convergent cosec cosine curve denoted determinant diameter divided eliminant ellipse equal equate coefficients expand factors figure formula function given circle given ratio Hence hyperbola imaginary roots infinite inscribed circle integer integral intersect inverse points limits logarithm method Multiply negative nine-point circle notation obtained orthogonally pair parabola parallel partial fractions perpendicular plane positive powers Proof Proof.—By Proof.—In Proof.—Let Proof.—The quantic quantities quotient radical axis radius respect result right angle rows Rule sides similar triangles Similarly sine singular solution solution squares substituting successive tangent Taylor's theorem theorem tion transformed triangle ABC unity vanishes variables zero