Practical Algebra (revised) Prepared for the Use of the Midshipmen at the United States Naval AcademyUnited States Naval Institute, 1910 - 191 páginas |
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Página 45
... approach any limit as more terms are taken , but increases indefinitely , so that we say that the sum is infinite . S∞∞ , if r > 1 , r < −1 , or r = 1 . Examples . 1. Find the sum to infinity of the progressions 80 6400 1 ,,, etc ...
... approach any limit as more terms are taken , but increases indefinitely , so that we say that the sum is infinite . S∞∞ , if r > 1 , r < −1 , or r = 1 . Examples . 1. Find the sum to infinity of the progressions 80 6400 1 ,,, etc ...
Página 46
... approaches closer and closer to a number L in such a way that the difference L - f ( x ) decreases indefi- nitely , f ( x ) is said to approach L as a limit . If there are two functions , f ( x ) 46 PRACTICAL ALGEBRA . 43-46 Limits ...
... approaches closer and closer to a number L in such a way that the difference L - f ( x ) decreases indefi- nitely , f ( x ) is said to approach L as a limit . If there are two functions , f ( x ) 46 PRACTICAL ALGEBRA . 43-46 Limits ...
Página 47
... approaches a limit 7 and F ( x ) approaches a limit L , f ( x ) ± F ( x ) , f ( x ) × F ( x ) , and l ± L , 1 × L , and— , respectively . f ( x ) F ( x ) approach the limits As limits behave in all these ways like particular values of ...
... approaches a limit 7 and F ( x ) approaches a limit L , f ( x ) ± F ( x ) , f ( x ) × F ( x ) , and l ± L , 1 × L , and— , respectively . f ( x ) F ( x ) approach the limits As limits behave in all these ways like particular values of ...
Página 48
... approach the limit zero ; in other words , the sum , difference or product of two infinitesimals is an infinitesimal . Again , if two variables are each increasing indefinitely , their sum and product are also in- creasing indefinitely ...
... approach the limit zero ; in other words , the sum , difference or product of two infinitesimals is an infinitesimal . Again , if two variables are each increasing indefinitely , their sum and product are also in- creasing indefinitely ...
Página 49
... approach zero as a limit , or the two may so balance each other that the fraction will approach some finite limit . ∞ The two forms and are therefore said to be indetermi- nate . - The following examples are typical of the treatment of ...
... approach zero as a limit , or the two may so balance each other that the fraction will approach some finite limit . ∞ The two forms and are therefore said to be indetermi- nate . - The following examples are typical of the treatment of ...
Otras ediciones - Ver todas
Practical Algebra (Revised) Prepared for the Use of the Midshipmen at the ... Stimson Joseph Brown,Paul Capron Sin vista previa disponible - 2016 |
Practical Algebra (Revised): Prepared for the Use of the Midshipmen at the ... Stimson J. Brown Sin vista previa disponible - 2016 |
Términos y frases comunes
abscissa angle asymptotes Binomial Theorem called chance of success chord circle computation conjugate constant convergent coordinates corresponding cubic function curve D₂ decimal places degree diameter difference distance divergent series divided draw ellipse equa Examples expression factors figure Find the equation Find the value function geometric progression give given number given point graph hence hyperbola identity imaginary infinite infinity integers intersections limiting tangent linear loga logarithm loge mantissa multiplying negative number number of terms parabola parallel partial fractions permutations perpendicular polynomial power-series proper fraction quadratic quadratic equation quotient real numbers real root region of convergence represented result rithms root of f(x)=0 simplified slope solution solve square root straight line surds synthetic division T₁ Theorem tion trace triangle undetermined coefficients value of f(x variable vertical vertical limiting x-axis y-axis y-intercept y=mx+b Y₁
Pasajes populares
Página 16 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 16 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Página 19 - Let N be a number whose integral part contains n digits ; then ff—. lQ(>ll)-hl lection . . ' . log N— (n - 1 ) + a fraction. Hence the characteristic is n — 1 ; that is, the characteristic of the logarithm of a number greater than unity is less by one than the number of digits in its integral part, and i& positive.
Página 20 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Página 90 - ... therefore 1 being the trigonometrical tangent of the angle made by the line with the axis of a;, this angle must be 45°, and the ordinate at the origin is 2.
Página 4 - In practice, the quotient of two complex numbers is usually found by multiplying both numerator and denominator by the conjugate of the denominator: o + ib _ a + ib c — id _ ac + bd be — ad . , . , n ^Md " F+ld
Página 56 - ... number of combinations of n things r at a time is the same as the number of combinations of n things n — r at a time ; This result is frequently useful in enabling us to abridge arithmetical work.
Página 23 - The cologarithm of a number is found by subtracting each figure of the logarithm from 9, except the last figure, which is subtracted from 10; then append — 10.
Página 53 - The various orders in which a number of things can be arranged are called their permutations. Thus...
Página 110 - ... in a few cases, to be hereafter pointed out, where oblique axes may be more advantageously employed. PROBLEM I. (8.) To find the equation of a straight line passing through a given point. Let us denote the coordinates of the given point by x...