Examples and Solutions in the Differential Calculus |
From inside the book
Results 1-3 of 12
Page 81
... hyperbola , is said to belong to hyperbolas of all orders . Find the subtangent at a given point in the curve . a xm = dx mxm - 1 .. dy anyn - 1 y2n an dx an dy mxm − 1.yn + 1 ' dx n a n n xm X. mxm- уп тхт - 1 m .. Subtan . NT = ydy ...
... hyperbola , is said to belong to hyperbolas of all orders . Find the subtangent at a given point in the curve . a xm = dx mxm - 1 .. dy anyn - 1 y2n an dx an dy mxm − 1.yn + 1 ' dx n a n n xm X. mxm- уп тхт - 1 m .. Subtan . NT = ydy ...
Page 93
... hyperbola , and a circle whose radius is 2a , have the same centre ; find the angle of intersection of the two curves . √15 4 Angle - tan - 1 . ( 37. ) Find that point in an ellipse at which the angle contained between the normal and ...
... hyperbola , and a circle whose radius is 2a , have the same centre ; find the angle of intersection of the two curves . √15 4 Angle - tan - 1 . ( 37. ) Find that point in an ellipse at which the angle contained between the normal and ...
Page 131
... hyperbola , referred to its asymptotes is xy = m2 ; find the radius of curvature . x dy dx m2 X d2y 2m2x 2m2 m2 : .p = 22 ' dy X + y = 0 , dx q = dx2 = x4 23 1 + p2 = 1 + m4 x4 + m2 24 x4 x4 + x2y2 204 x2 + y2 x2 : . R = ( 1 + p2 ) ...
... hyperbola , referred to its asymptotes is xy = m2 ; find the radius of curvature . x dy dx m2 X d2y 2m2x 2m2 m2 : .p = 22 ' dy X + y = 0 , dx q = dx2 = x4 23 1 + p2 = 1 + m4 x4 + m2 24 x4 x4 + x2y2 204 x2 + y2 x2 : . R = ( 1 + p2 ) ...
Contents
Binomial theorem examples | 1 |
successive | 15 |
Lagranges notation of Taylors theorem | 16 |
7 other sections not shown
Other editions - View all
Common terms and phrases
1+p² 1+x² a²-x² a²+b² a²+x² a²y angle asymptote asymptotic circle axes centre chord co-ordinates common parabola constant contrary flexure coseco cosx cuts the axis d²u d2u d2u d2y dx2 d³u diameter differential coefficient distance draw du du dx d2u dx dy dx dz dx² dx2 dy2 dy dy dy dz e²x² eliminate ellipse equal evolute find the equation function given Hence hyperbola Inscribe the greatest intersection J. F. HEATHER latus rectum locus logarithmic maxima and minima maximum or minimum normal NP=y origin osculating circle perpendicular point of contrary polar equation positive prove radius of curvature right-angles Scott Burn secx semicubical parabola sinx spiral straight line substituting subtangent tangent Taylor's theorem trace the curve triangle variable vertex x²+y2 x²y