1. State Leibnity's theorem on Leigher derivatives: If y sin (m sin x) then show that...

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1. State Leibnity's theorem on Leigher derivatives: If y sin (m sin x) then show that (1-x) Ya+2 (2n+1) xyn+1 + (m-n)yn = 0 2. Assuming the validity of expansion, find the expansion of the function ex by Maclaurin's 1+e* theorem. 3. Evaluate lim xe (1+x)log(1+x) x 4. Find the asymptotes of the curve y +2xy+xy-y+1=0 5. Find the radius of curvature of the curve y=x(x-3) at the points where the tangent is parallel to x-axis OR Find the pedal equation of the curve r = a cos20 dx II 6. Show that = x+a-x2 4 1. State Leibnity's theorem on Leigher derivatives: If y sin (m sin x) then show that (1-x) Ya+2 (2n+1) xyn+1 + (m-n)yn = 0 2. Assuming the validity of expansion, find the expansion of the function ex by Maclaurin's 1+e* theorem. 3. Evaluate lim xe (1+x)log(1+x) x 4. Find the asymptotes of the curve y +2xy+xy-y+1=0 5. Find the radius of curvature of the curve y=x(x-3) at the points where the tangent is parallel to x-axis OR Find the pedal equation of the curve r = a cos20 dx II 6. Show that = x+a-x2 4