1. If ya cos (logx) + b sin (logx). Prove that x. yn+2 + (2n+1)x. yn+1...

Transcribed Image Text:

1. If ya cos (logx) + b sin (logx). Prove that x. yn+2 + (2n+1)x. yn+1 + (n + 1)yn = 0. 2. State and prove Rolle's theorem. 3. Determine the values of a, b, c, so that Lt (a+bcos x)x - c. sin x = 1. 0+x 5 X 4. Find the asymptotes of the curve (x + y) (x + 2y + 2) = x+9y-2. 5. If e and e be the radii of curvature at the ends of a focal chord of the parabola y = 4ax, prove that e + 22/3 = (2a)-2/3 -2/3 T x tan x 6. Prove that dx = sec x+coS X 4 1. If ya cos (logx) + b sin (logx). Prove that x. yn+2 + (2n+1)x. yn+1 + (n + 1)yn = 0. 2. State and prove Rolle's theorem. 3. Determine the values of a, b, c, so that Lt (a+bcos x)x - c. sin x = 1. 0+x 5 X 4. Find the asymptotes of the curve (x + y) (x + 2y + 2) = x+9y-2. 5. If e and e be the radii of curvature at the ends of a focal chord of the parabola y = 4ax, prove that e + 22/3 = (2a)-2/3 -2/3 T x tan x 6. Prove that dx = sec x+coS X 4