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11 psl.
... curve f ( x , y ) = 0 . that the curves x2 + y2 = 2a2 log x + c cut the ellipses x2 12 a2 + a2 + λ = 1 orthogonally . 4. ( a ) In polars prove ( i ) tan = rf ' . ( ii ) p = r2 \\ / r2 + ƒ'2 . ( b ) Find the p , r equation of the ...
... curve f ( x , y ) = 0 . that the curves x2 + y2 = 2a2 log x + c cut the ellipses x2 12 a2 + a2 + λ = 1 orthogonally . 4. ( a ) In polars prove ( i ) tan = rf ' . ( ii ) p = r2 \\ / r2 + ƒ'2 . ( b ) Find the p , r equation of the ...
psl.
... curve . 5. Show that if a curve of n dimensions has n non- parallel asymptotes , these intersect the curve in n points which lie on a curve of n 2 dimensions . ― 6. Prove that at a point of contrary flexure u + d2u / d02 changes sign ...
... curve . 5. Show that if a curve of n dimensions has n non- parallel asymptotes , these intersect the curve in n points which lie on a curve of n 2 dimensions . ― 6. Prove that at a point of contrary flexure u + d2u / d02 changes sign ...
psl.
... Ə2u / Əxǝy , & c . 8. Define the osculating plane of a curve of double curvature at a given point , and find its equation . TRIGONOMETRY II . FINAL HONOURS . I. In the series Queen's University Examinations : April , 1909 .
... Ə2u / Əxǝy , & c . 8. Define the osculating plane of a curve of double curvature at a given point , and find its equation . TRIGONOMETRY II . FINAL HONOURS . I. In the series Queen's University Examinations : April , 1909 .
psl.
... curve 2x2 − 3xy + 8x3 −y3 = 0 as to nodes or cusps , and represent by a graph . 7. ( a ) Find the radius of curvature for the curve given by the parametric equations x = ft , y = $ t ; ( b ) apply to the case where x = I cos 0 , y = 1 ...
... curve 2x2 − 3xy + 8x3 −y3 = 0 as to nodes or cusps , and represent by a graph . 7. ( a ) Find the radius of curvature for the curve given by the parametric equations x = ft , y = $ t ; ( b ) apply to the case where x = I cos 0 , y = 1 ...
psl.
... curve a3y2 = ( b + x ) x4 . 4. Find the volume described by one revolution of ( y2 + x2 ) 2 a2 ( x2 -2 ) = o about the x - axis between lts . 2 o and a . 5. The cardioid r = a ( 1+ cos ) revolves about the prime vector . Find the ...
... curve a3y2 = ( b + x ) x4 . 4. Find the volume described by one revolution of ( y2 + x2 ) 2 a2 ( x2 -2 ) = o about the x - axis between lts . 2 o and a . 5. The cardioid r = a ( 1+ cos ) revolves about the prime vector . Find the ...
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