Bokky
Member
hi guys, just skimming thru my 3U half yearly which i did pretty poorly in, ive got a few questions from it which will appear in my next test so i gotta learn them now.
1) parabola x^2 = 4y. The tangent to the parabola at P(2p, p^2), p>0 cuts the x axis at A. The normal to the parabola at P cuts the y axis at B.
(i) Derive the equation of the tangent AP.
(ii) Show that B has the coordinates (0, p^2+2).
(iii) Let C be the midpoint of AB. Find the cartesian equation of the locus of C.
2) The region bounded by y = 3sin x, the x axis and the line x= pie/2 is rotated about the x axis to form a solid. Calculate the volume of solid (leave answer in exact form).
3)The following area is rotated about the y-axis.
y=3x^2 ; y=16-x^2
Show that the volume of the solid of revolution is 32pie units^3
4) (i) By equating the coefficients of sinx and cosx or otherwise, find the constants A and B satisfying the identity
A(2sinx+cosx)+B(2cosx-sinx)==sinx+8cosx
(ii) Hence evaluation int. (sinx+8cosx)/(2sinx+cosx)dx
LOL have fun, ta guys![Big Grin :D :D](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
1) parabola x^2 = 4y. The tangent to the parabola at P(2p, p^2), p>0 cuts the x axis at A. The normal to the parabola at P cuts the y axis at B.
(i) Derive the equation of the tangent AP.
(ii) Show that B has the coordinates (0, p^2+2).
(iii) Let C be the midpoint of AB. Find the cartesian equation of the locus of C.
2) The region bounded by y = 3sin x, the x axis and the line x= pie/2 is rotated about the x axis to form a solid. Calculate the volume of solid (leave answer in exact form).
3)The following area is rotated about the y-axis.
y=3x^2 ; y=16-x^2
Show that the volume of the solid of revolution is 32pie units^3
4) (i) By equating the coefficients of sinx and cosx or otherwise, find the constants A and B satisfying the identity
A(2sinx+cosx)+B(2cosx-sinx)==sinx+8cosx
(ii) Hence evaluation int. (sinx+8cosx)/(2sinx+cosx)dx
LOL have fun, ta guys