1. State Leibnitz's theorem on heigher order derivative. If y=ealanx, (1+x2)+2+(2nx+2x-a)yn+1+n(n+1)y =0 prove that 2. State...

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1. State Leibnitz's theorem on heigher order derivative. If y=ealanx, (1+x2)+2+(2nx+2x-a)yn+1+n(n+1)y =0 prove that 2. State difference between Roll's Theorem and Lagrange's Mean value theorem. Verify Lagrange's mean value theorem for f(x) = x(x-1)(x-2) when xe 3. Define inderminate form of a function. Evaluate lim tanx x 0 4. Define asymptote to a curve. Find the asymptotes of curve. y3+2xy+x2y-y+1=0. 5. Find radius of curvature of the curve x3+ y3=3axy at origin. OR Find the pedal equation of the polar curve r = a cosme. 6. Integrate: cosx dx (1 + sin x)(2+ sin x) 1. State Leibnitz's theorem on heigher order derivative. If y=ealanx, (1+x2)+2+(2nx+2x-a)yn+1+n(n+1)y =0 prove that 2. State difference between Roll's Theorem and Lagrange's Mean value theorem. Verify Lagrange's mean value theorem for f(x) = x(x-1)(x-2) when xe 3. Define inderminate form of a function. Evaluate lim tanx x 0 4. Define asymptote to a curve. Find the asymptotes of curve. y3+2xy+x2y-y+1=0. 5. Find radius of curvature of the curve x3+ y3=3axy at origin. OR Find the pedal equation of the polar curve r = a cosme. 6. Integrate: cosx dx (1 + sin x)(2+ sin x)