Advanced Algebra for Colleges and SchoolsAmerican Book Company, 1902 - 608 páginas |
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Página 6
... OF SERIES 496 UNDETERMINED COEFFICIENTS 509 EXPONENTIAL AND LOGARITHMIC SERIES 524 SUMMATION OF SERIES 533 FUNCTIONS OF A SINGLE VARIABLE 545 THEORY OF EQUATIONS 562 ALGEBRAIC SOLUTIONS If 1. PROBLEM 1. A man had 400 6 CONTENTS.
... OF SERIES 496 UNDETERMINED COEFFICIENTS 509 EXPONENTIAL AND LOGARITHMIC SERIES 524 SUMMATION OF SERIES 533 FUNCTIONS OF A SINGLE VARIABLE 545 THEORY OF EQUATIONS 562 ALGEBRAIC SOLUTIONS If 1. PROBLEM 1. A man had 400 6 CONTENTS.
Página 379
... function of x and z . Every function of a single variable is a variable . 1 are also 1 -x The variable to which different values may be given at pleasure or according to some law is called the Independent Variable , and the function of ...
... function of x and z . Every function of a single variable is a variable . 1 are also 1 -x The variable to which different values may be given at pleasure or according to some law is called the Independent Variable , and the function of ...
Página 384
... function of x approach as near as we please to a finite constant 1 , 7 is called the limit of the function when xa . Suppose that .1 , .11 , .111 , .1111 , ... are successive values of x approaching as a limit . Then , the corresponding ...
... function of x approach as near as we please to a finite constant 1 , 7 is called the limit of the function when xa . Suppose that .1 , .11 , .111 , .1111 , ... are successive values of x approaching as a limit . Then , the corresponding ...
Página 385
... k is any constant , ∞ , + k Hence , ∞ - < = ∞g ; .. ∞02 - --- 0 ' 0 × ∞ , and ∞1 = k . is a symbol for an indeterminate number . ADV . ALG . - 25 429. Since every function of a single variable is a VARIABLES AND LIMITS 385.
... k is any constant , ∞ , + k Hence , ∞ - < = ∞g ; .. ∞02 - --- 0 ' 0 × ∞ , and ∞1 = k . is a symbol for an indeterminate number . ADV . ALG . - 25 429. Since every function of a single variable is a VARIABLES AND LIMITS 385.
Página 386
... function 4x employed directly to evaluate the functions -- - 3y . 3 y is found by substi- But if substitution is 1 1 × Y , and x a 1 x ( x - 1 ) y ( x2 − 1 ) ÷ ( x 1 ) when x1 and y = 0 , these functions take the forms ∞ - ∞ , ∞ × 0 ...
... function 4x employed directly to evaluate the functions -- - 3y . 3 y is found by substi- But if substitution is 1 1 × Y , and x a 1 x ( x - 1 ) y ( x2 − 1 ) ÷ ( x 1 ) when x1 and y = 0 , these functions take the forms ∞ - ∞ , ∞ × 0 ...
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Términos y frases comunes
a²b² a²x² ab² absolutely convergent algebraic sum arithmetical means arithmetical progression ax² binomial called cents coefficients column Commutative Law complex numbers continued fraction convergent convergent series cube root denominator difference digits divided dividend divisible established as follows EXAMPLES exponent expression factor Find the sum Find the value finite formula function geometrical mean geometrical progression geometrical series given equation Hence highest common divisor imaginary numbers inequality integer last term limit logarithm multiplied negative number nth root number of terms numerically less obtained polynomial positive integer positive number positive root PRINCIPLE quadratic quotient ratio real number reduced remainder represent result second term SOLUTION square root Substituting subtracted surd third Transposing twice units unknown number variable x²y x²y²
Pasajes populares
Página 212 - ... and if the number is divided by the sum of its digits, the quotient is 21 and the remainder 4.
Página 134 - Multiplying or dividing both terms of a fraction by the same number does not change the value of the fraction.
Página 343 - ... that the volume of a sphere varies as the cube of its radius. 20. Find the radius of a sphere whose volume is equal to the sum of the volumes of three spheres whose radii are r, /, and r".
Página 41 - A term may be transposed from one member of an equation to the other, provided its sign is changed.
Página 435 - The number of permutations of n different things taken r at a time is denoted by „Pr.
Página 424 - The logarithm of a quotient is found by subtracting the logarithm of the divisor from that of the dividend.
Página 40 - The process of changing a term from one member of an equation to the other is called Transposition.
Página 331 - PRINCIPLE 7. — If four numbers are in proportion, the. difference between the terms of the first ratio is to either term of the first ratio as the difference between the terms of the second ratio is to the corresponding term of the second ratio ; that is, the numbers are in proportion by Division.
Página 323 - A farmer has two cubical granaries. The side of one is 3 yards longer than the side of the other, and the difference in their solid contents is 117 cubic yards.
Página 426 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.