A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
From inside the book
Results 6-10 of 16
Page 257
... critical values of x and y which satisfy ( 12 ) be x 。 and dr dx X yo ; we have to examine the change of sign which ( 4 ) dr undergo at these values . In certain cases this change may be conveniently determined by an examination of the ...
... critical values of x and y which satisfy ( 12 ) be x 。 and dr dx X yo ; we have to examine the change of sign which ( 4 ) dr undergo at these values . In certain cases this change may be conveniently determined by an examination of the ...
Page 258
... critical values , that ( d ) 258 MAXIMA AND MINIMA OF [ 159 . Application of the method to total minima.
... critical values , that ( d ) 258 MAXIMA AND MINIMA OF [ 159 . Application of the method to total minima.
Page 259
Bartholomew Price. vanish at the critical values , that ( d ) = 0 , and D dr D dx dy = and that ( d ) and ( d ) should be positive ; accordingly , dx dx dy dy - following the process of the last Article , the two values of 0 , and ...
Bartholomew Price. vanish at the critical values , that ( d ) = 0 , and D dr D dx dy = and that ( d ) and ( d ) should be positive ; accordingly , dx dx dy dy - following the process of the last Article , the two values of 0 , and ...
Page 260
... values as exist at the critical values of the variables . If all the second derived - functions of the original function vanish at the critical values , the preceding results come to nought as however I have alluded to this case in Art ...
... values as exist at the critical values of the variables . If all the second derived - functions of the original function vanish at the critical values , the preceding results come to nought as however I have alluded to this case in Art ...
Page 262
... critical values of 0 and 4 give a maximum : and as 0 = - π Φ 6 the triangle is equilateral . Hence the greatest triangle that can be inscribed in a circle is the equilateral one . 2 162. ] In the case in which ( 127 ) ( 124 ) – ( 17 ) ...
... critical values of 0 and 4 give a maximum : and as 0 = - π Φ 6 the triangle is equilateral . Hence the greatest triangle that can be inscribed in a circle is the equilateral one . 2 162. ] In the case in which ( 127 ) ( 124 ) – ( 17 ) ...
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Common terms and phrases
according algebraical angles applicable assume axis becomes Calculus called changes sign Chapter circle coefficients consider constant continuous corresponding curve derived derived-functions determine differential dimensions direction divided drawn dx dy dy dx elimination equal equation examples expression factors finite function geometrical given gives greater Hence homogeneous function increases independent infinite infinitesimal infinity involved less limit maxima maximum means method minima minimum value negative observed origin partial particular pass plane positive powers preceding properties quantity relation replaced represent respectively result roots sides similar Similarly singular value straight line substituted successive suppose symbols tangent Theorem tion true values vanish variables variation vary whence zero