Differential Calculus with Applications and Numerous Examples: An Elementary Treatise... |
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Page 6
... shows 1+ X The expression can also be written that if x be increased indefinitely it can be made to continually approach and to differ by less than any assignable quantity from 2 , which is therefore its limit in that case . Ex . 3. The ...
... shows 1+ X The expression can also be written that if x be increased indefinitely it can be made to continually approach and to differ by less than any assignable quantity from 2 , which is therefore its limit in that case . Ex . 3. The ...
Page 17
... Show that the co - ordinates of any point on the rectangular hyperbola x2 - y2 = a2 may be denoted by a cosh 0 , a sinh 0 . 3. Prove ( a ) sinh - 1x = tanh XC - √1 + x2 ( b ) 2tanh - 1 = log X 1 + % 1 X INFINITESIMALS . 26. All ...
... Show that the co - ordinates of any point on the rectangular hyperbola x2 - y2 = a2 may be denoted by a cosh 0 , a sinh 0 . 3. Prove ( a ) sinh - 1x = tanh XC - √1 + x2 ( b ) 2tanh - 1 = log X 1 + % 1 X INFINITESIMALS . 26. All ...
Page 24
... Hence the difference of the arc AB and the chord AB , which is less than that between AP + PB and the chord AB , must be at least of the third order . EXAMPLES . 1. Show that , in the figure of 24 DefinitioNS . LIMITS .
... Hence the difference of the arc AB and the chord AB , which is less than that between AP + PB and the chord AB , must be at least of the third order . EXAMPLES . 1. Show that , in the figure of 24 DefinitioNS . LIMITS .
Page 25
... show that the triangle PMQ is of the fifth order of smallness . 3. A straight line of constant length slides between two straight lines at right angles , viz . , CAa , CbB ; AB and ab are two positions of the line and P their point of ...
... show that the triangle PMQ is of the fifth order of smallness . 3. A straight line of constant length slides between two straight lines at right angles , viz . , CAa , CbB ; AB and ab are two positions of the line and P their point of ...
Page 37
... Show that if so sin ut , where μ is a constant , the rate of in- crease of the velocity is proportional to the distance of the particle measured along its path from a fixed position . 45. It will often be convenient in proving standard ...
... Show that if so sin ut , where μ is a constant , the rate of in- crease of the velocity is proportional to the distance of the particle measured along its path from a fixed position . 45. It will often be convenient in proving standard ...
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Differential Calculus With Applications and Numerous Examples: An Elementary ... Joseph Edwards No preview available - 2006 |
Common terms and phrases
A. W. VERRALL ALGEBRA angle ARITHMETIC Assistant-Master asymptote axis BEGINNERS BOOK Cambridge CHEMISTRY chord Christ's College circle Clifton College co-ordinates conic Crown 8vo curvature cusp d²y denote differential coefficient dx dx dx dy dx² dy dx ELEMENTARY English EXAMPLES expansion Extra fcap Fcap Fellow of St Fellow of Trinity function Geometrical given Globe 8vo Greek Hence HISTORY independent variable John's College late Fellow LATIN Lecturer LL.D Macmillan's Master Mathematics normal origin Owens College Oxford p(x+h parabola pedal equation perpendicular point of inflexion polar positive pedal PRIMER Professor prove quantity radius School Second Edition Show straight line tangent Taylor's Theorem Translated TREATISE Trinity College University University of Cambridge Vocabulary ди ди ду дх эф Эх
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