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# The Principles Of The Differential And Integral Calculus; Simplified, And Applied To The Solution…

## byThomas Turner Tate

### Paperback | January 22, 2013

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1863 edition. Excerpt: ... x=a. l + (a + x? 1 + 2a Thus by an easy algebraic process we may frequently find the value of a vanishing fraction; the method, however, derived from the differential calculus is more general, and in many difficult cases much more simple in practice. fix) 0 Let u=-t-±--( be a vanishing fraction which becomes T(x) 0 when x=a. df(x) ' u dr()-df(x). u-dx dx dx' dv(x)' dx Hence we have the following rule. To find the value of a vanishing fraction, divide the differencial coefficient of the numerator by the differential coefficient of the denominator, and then substitute the given value for the variable. Should it be found, after this process, that the fraction still vanishes the process may obviously be repeated until the fraction ceases to have the vanishing form. Ex. 1. Find the value of u=-i--jr-x s, when x=l. x3 + 2x2--x--2 Here the differential coefficient of the numerator is 3x2; and that of the denominator 3x'+4x--1, 3x2 1, " u=o i, A,--S, when x--l. 3x2+4x--1 2 2. u--=--=5, when x=2. X £iX %n 3. u=,--n when x=. 1-x 2_.2 #4-1 4. Find the value of u= xi_2aa+x2, wnen--Here it will be necessary to differentiate twice. 3a?-2a;-l The result of the first differentiations is TANGENTS TO CURVES. 75. To draw a tangent to a given point P of the plane curve Apq referred to the rectangular axes Ax and Ay. Let Ft be the tangent, cutting the axis of x in the point T, then by Art. 32. we have B In order to draw the tangent Pt it is only necessary that we should find the point T, or the distance NT which is called the subtangent; for this purpose we have dy tanNTPXNT=NP, or XNT=y,.. Nt or subtangent---J? (2) The length of the tangent is found from the equation The length of the normal is found from the equation. Examples. 1. To draw a...

### Details & Specs

Title:The Principles Of The Differential And Integral Calculus; Simplified, And Applied To The Solution…Format:PaperbackDimensions:24 pages, 9.69 × 7.44 × 0.05 inPublished:January 22, 2013Publisher:General Books LLCLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:1234384728

ISBN - 13:9781234384722

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