Differential Calculus with Applications and Numerous Examples: An Elementary Treatise...Macmillan, 1886 - 439 páginas |
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Página 107
... root of the equation ' ( x ) = 0 lies between every adjacent two of the real roots of the equation p ( x ) = 0 " ; and is known as Rolle's Theorem . 120. Remainder after the first n terms have been taken from Taylor's Series . There is ...
... root of the equation ' ( x ) = 0 lies between every adjacent two of the real roots of the equation p ( x ) = 0 " ; and is known as Rolle's Theorem . 120. Remainder after the first n terms have been taken from Taylor's Series . There is ...
Página 121
... root of an equation f ( x ) = 0 can lie between any adjacent two of the roots of the equation f ' ( x ) = 0 . 43. Show that the following expressions are positive for all positive values of x : ( i . ) ( x − 1 ) e2 + 1 ; - ( ii . ) ( x ...
... root of an equation f ( x ) = 0 can lie between any adjacent two of the roots of the equation f ' ( x ) = 0 . 43. Show that the following expressions are positive for all positive values of x : ( i . ) ( x − 1 ) e2 + 1 ; - ( ii . ) ( x ...
Página 164
... roots giving the directions in which the several branches of the curve pass through the origin . If m1 , m „ m3 , ... m , be the roots , the equations of the several tangents are y = m1x , y 164 TANGENTS AND NORMALS .
... roots giving the directions in which the several branches of the curve pass through the origin . If m1 , m „ m3 , ... m , be the roots , the equations of the several tangents are y = m1x , y 164 TANGENTS AND NORMALS .
Página 187
... roots . The condition for this will be found by eliminating x between 4 ( x ) = 0 and p ′ ( x ) = 0 . In following this method , instead of eliminating y it is often better to make a homogeneous equation between F ( x , y ) = 0 and lx + ...
... roots . The condition for this will be found by eliminating x between 4 ( x ) = 0 and p ′ ( x ) = 0 . In following this method , instead of eliminating y it is often better to make a homogeneous equation between F ( x , y ) = 0 and lx + ...
Página 204
... roots . μ12zg If , then , M. , μn be the n values of u deduced from equation ( E ) ( which is of the nth degree in μ ) , the corresponding values of ẞ will in general be given by ß1 = Pn - 1 ( u , ) φη ( μ . ) , B2 = Pn - 1 ( μ2 ) P'n ...
... roots . μ12zg If , then , M. , μn be the n values of u deduced from equation ( E ) ( which is of the nth degree in μ ) , the corresponding values of ẞ will in general be given by ß1 = Pn - 1 ( u , ) φη ( μ . ) , B2 = Pn - 1 ( μ2 ) P'n ...
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Differential Calculus With Applications and Numerous Examples: An Elementary ... Joseph Edwards Sin vista previa disponible - 2006 |
Términos y frases comunes
ALGEBRA angle Assistant-Master asymptote axis Cambridge cardioide centre chord circle co-ordinates coincident points conic Crown 8vo cusp cuts the curve cycloid denote differential coefficient dx dx dx dy dy dx ELEMENTARY ellipse envelope EXAMPLES Extra fcap fcap Fellow of Trinity Find function Globe 8vo Hence hyperbola independent variable infinite intersection intrinsic equation inverse John's College late Fellow limit LL.D locus MACMILLAN'S EDUCATIONAL CATALOGUE Mathematics maxima and minima minimum value negative normal ordinate origin Owens College p(x+h parabola parallel pedal equation perpendicular point of contact point of inflexion polar positive pedal PRIMER Professor prove quantity radius of curvature revised School Show straight line tangent Taylor's Theorem Trace the curve Trinity College ultimately coincident vanish whence zero ди ди ду дх Эф
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