## The Analyst: A Monthly Journal of Pure and Applied Mathematics, Volumes 3-4Pierson & Blair, 1876 |

### From inside the book

Results 1-5 of 29

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**zero**. The area between the first and third ordi- nates , the axis of x and the curve is ( x +24 ) 3 — x3 3p or 46x2 + 124x + 842 4x2 - 3 Р = 3 P + 4 . + ( x + 4 ) 2 ( x + 24 ) 2 ̄ p P Area = 4 ( yo + 4y1 + Y2 ) . This result has been ... Page 6

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**zero**. ( 8 ) . Let us take a function of r which shall produce the given values of y when x has certain values . The form which Lagrange employs in his method of interpolation gives , denoting by a , a1 , a2 , & c . the given values of ... Page 8

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**zero**, and the error in the quadrature will be 2.4 ( x ) dx . Since Q does not ex- ceed the degree n -1 in order that the error may be**zero**we determine 4 ( x ) by the conditions , - 0 , S'xq ( x ) dx = 0 , S ' 4 ( x ) dx = 0 , 0 S'a ... Page 9

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**zero**between the limits 0 and 1 the integrals sy ( x ) dx , ƒ3y ( x ) dx3 . f ( x ) dx must vanish for the same limits . We have therefore to find a function such that the function itself and its 1st , 2nd , 3rd , and nth differentials ... Page 14

... development must commence with the

... development must commence with the

**zero**power of ( x - x ' ) since it must reduce to ( x ' ) when x = x ' ; whence u ― u ' = y ( x ) —y ( x ' ) = P ( x — x ' ) + Q ( x — x ' ) 3 + & c . In the same manner as before we get du ' -14-### Other editions - View all

### Common terms and phrases

5th degree a₁ algebraic ANALYST angle ARTEMAS MARTIN assumed axis b₁ C₁ circular coefficients common logarithms constant curve denote determine differential distance E. B. SEITZ ellipse Elliptic Functions equal equation expression factor formula function given circle gives hence hyperbola integral intersection inverse Lagrange's Theorem locus logarithms method multiply observations orbital orbital force ORSON PRATT oxen parabola parallel perpendicular plane points at infinity position probable error quadrics quadrilateral radius ratio reduce represent result roots sides SOLUTION BY PROF SOLUTIONS of problems sphere square substitution surface tangent Taylor's Theorem Theorem tion triangle UNION SPRINGS unknown quantities values velocity whence zero