College AlgebraScott, Foresman, 1901 - 777 páginas |
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Página vi
... limit , and upon the rigorous proof of the theorem of undetermined coefficients . Attention is directed to the fact that the sum of an infinite series is the limit of a variable sum ; to the geometric illustrations of the derivation and ...
... limit , and upon the rigorous proof of the theorem of undetermined coefficients . Attention is directed to the fact that the sum of an infinite series is the limit of a variable sum ; to the geometric illustrations of the derivation and ...
Página xiv
... LIMITS System of Rational Numbers Insufficient 337 Introduction 338 Properties of the Series which define r Limit A 343 B 343 Irrational Numbers 344 Zero , Positive , and Negative . 345 Addition , Subtraction , Multiplication , and ...
... LIMITS System of Rational Numbers Insufficient 337 Introduction 338 Properties of the Series which define r Limit A 343 B 343 Irrational Numbers 344 Zero , Positive , and Negative . 345 Addition , Subtraction , Multiplication , and ...
Página xviii
... LIMITS AND SERIES CHAPTER I LIMITS Constants - Variables - Limits 623 Infinitesimals and Infinites - Theorems concerning the same 625 CHAPTER II CONVERGENCE Definition of an Infinite Series . 630 Convergence of Series whose Terms are ...
... LIMITS AND SERIES CHAPTER I LIMITS Constants - Variables - Limits 623 Infinitesimals and Infinites - Theorems concerning the same 625 CHAPTER II CONVERGENCE Definition of an Infinite Series . 630 Convergence of Series whose Terms are ...
Página 45
... limit to the field of subtraction , making its range much narrower than that of addition . This limitation restricts the use of equations 1-5 of 238 to particular classes of values . For example , such a simple inference as 2a ( 2a + 3b ) ...
... limit to the field of subtraction , making its range much narrower than that of addition . This limitation restricts the use of equations 1-5 of 238 to particular classes of values . For example , such a simple inference as 2a ( 2a + 3b ) ...
Página 68
... limits as to make division an unimportant operation as compared with addition , multiplication , and subtraction as dis- cussed in Chapter III . This restriction on division can be removed in the same way as subtraction was generalized ...
... limits as to make division an unimportant operation as compared with addition , multiplication , and subtraction as dis- cussed in Chapter III . This restriction on division can be removed in the same way as subtraction was generalized ...
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Términos y frases comunes
A₁ algebraic Arithmetic ax² b₁ binomial Binomial Theorem c₁ CHAPTER coefficients common convergent corresponding cube root decimal definition denominator determinant difference divided division divisor equal equivalent example exponent expression factors figures Find the number formula fraction given equation greater Hence imaginary increases inequality integer irrational less limit log 1+r logarithm mantissa mathematical induction monomial multiplied negative number nth root number of terms P₁ partial fractions polynomial positive integer positive number problem quadratic quadratic equation quotient rational remainder result rule satisfy second degree second member solution Solve the equations square root substituting subtraction Suppose surd symbols system of equations theorem third tion triangle trinomial unknown numbers unknown quantities Va² zero
Pasajes populares
Página 205 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Página 666 - Q(x) to obtain a quotient (polynomial of the form -Q ) plus a rational function (remainder divided by the divisor) in which the degree of the numerator is less than the degree of the denominator.
Página 79 - Raise the absolute value of the numerical coefficient to the required power, and multiply the exponent of each letter by the exponent of the required power.
Página 71 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Página 588 - What will $ 100 amount to in 7 years with interest at 8% per annum, compounded semi-annually ? 3. In how many years will a sum of money double itself at 6%, compounded annually ? 4.
Página 181 - A person has a hours at his disposal. How far may he ride in a coach which travels b miles an hour, so as to return home in time, walking back at the rate of с miles an hour ? 43.
Página 519 - In any proportion, the terms are in proportion by Alternation; that is, the first term is to the third as the second term is to the fourth.
Página 520 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Página 524 - The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples...
Página 588 - June, 1889.) 1. In how many years will a sum of money double itself at 4 per cent., interest being compounded semi-annually ? 2.