1. State Leibnitz theorem. If log y = tanx, then show that (1+x)yn+2+(2nx+2x-1)y++(n+n)y = 0 [1+4]...

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1. State Leibnitz theorem. If log y = tanx, then show that (1+x)yn+2+(2nx+2x-1)y++(n+n)y = 0 [1+4] [1+2+2] [1+4] [5] [5] [5] 2. State Rolle's theorem. Is the theorem true when the function is not continuous at the end points? Justify your answer. Verify Rolle's theorem for f(x)=x25x+6 on [2,3]. lim 3. State L-Hospital's rule. Evaluate x 1(2-x) tan 4. Find the asymptotes of the curve (x+y)2(x+2y+2)=x+9y-2 5. Find the pedal equation of the ellipse + x y2 = 1. b 6. Evaluate the integral dx 7. Apply the rule of differentiation under integral sign to evaluate sin x deduce that dx= 2 ax sin x dx and hence [5] 1. State Leibnitz theorem. If log y = tanx, then show that (1+x)yn+2+(2nx+2x-1)y++(n+n)y = 0 [1+4] [1+2+2] [1+4] [5] [5] [5] 2. State Rolle's theorem. Is the theorem true when the function is not continuous at the end points? Justify your answer. Verify Rolle's theorem for f(x)=x25x+6 on [2,3]. lim 3. State L-Hospital's rule. Evaluate x 1(2-x) tan 4. Find the asymptotes of the curve (x+y)2(x+2y+2)=x+9y-2 5. Find the pedal equation of the ellipse + x y2 = 1. b 6. Evaluate the integral dx 7. Apply the rule of differentiation under integral sign to evaluate sin x deduce that dx= 2 ax sin x dx and hence [5]