11X1 T09 08 implicit differentiation (2011)

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<ul><li> 1. Differentiability </li> <li> 2. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous i.e. lim f x lim f x x a x a </li> <li> 3. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous i.e. lim f x lim f x x a x a y y x 1 1 1 x </li> <li> 4. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous i.e. lim f x lim f x x a x a y y x 1 1 1 x not differentiable at x = 1 </li> <li> 5. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous i.e. lim f x lim f x x a x a y y x 1 1 1 x not differentiable at x = 1 lim f x 1 x1 </li> <li> 6. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous i.e. lim f x lim f x x a x a y y x 1 1 1 x not differentiable at x = 1 lim f x 1 lim f x 1 x1 x1 </li> <li> 7. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous i.e. lim f x lim f x x a x a y y y x2 y x 1 1 1 x x not differentiable at x = 1 lim f x 1 lim f x 1 x1 x1 </li> <li> 8. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous i.e. lim f x lim f x x a x a y y y x2 y x 1 1 1 x 1 x not differentiable at x = 1 lim f x 1 lim f x 1 x1 x1 </li> <li> 9. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous i.e. lim f x lim f x x a x a y y y x2 y x 1 1 1 x 1 x not differentiable at x = 1 differentiable at x = 1 lim f x 1 lim f x 1 x1 x1 </li> <li> 10. Implicit Differentiation </li> <li> 11. Implicit Differentiation df df dy dx dy dx </li> <li> 12. Implicit Differentiation df df dy dx dy dxe.g. (i) x y 2 </li> <li> 13. Implicit Differentiation df df dy dx dy dxe.g. (i) x y 2 x y d d 2 dx dx </li> <li> 14. Implicit Differentiation df df dy dx dy dxe.g. (i) x y 2 x y d d 2 dx dx d 2 dx y dy y dx d 2 dy </li> <li> 15. Implicit Differentiation df df dy dx dy dxe.g. (i) x y 2 x y d d 2 dx dx dy 1 2y dx d 2 dx y dy y dx d 2 dy </li> <li> 16. Implicit Differentiation df df dy dx dy dxe.g. (i) x y 2 x y d d 2 dx dx dy 1 2y dx dy 1 dx 2 y d 2 dx y dy y dx d 2 dy </li> <li> 17. Implicit Differentiation df df dy dx dy dxe.g. (i) x y 2 (ii) dx x y d 2 3 x y d d 2 dx dx dy 1 2y dx dy 1 dx 2 y d 2 dx y dy y dx d 2 dy </li> <li> 18. Implicit Differentiation df df dy dx dy dxe.g. (i) x y 2 (ii) dx x y d 2 3 x y d d 2 x2 3 y 2 y3 2 x dx dx dy dy dx 1 2y dx dy 1 dx 2 y d 2 dx y dy y dx d 2 dy </li> <li> 19. Implicit Differentiation df df dy dx dy dxe.g. (i) x y 2 (ii) dx x y d 2 3 x y d d 2 x2 3 y 2 y3 2 x dx dx dy dy dx 1 2y 2 2 dy dx 3x y 2 xy 3 dy 1 dx dx 2 y d 2 dx y dy y dx d 2 dy </li> <li> 20. iii Find the equation of the tangent to x 2 y 2 9 at the point 1, 2 2 </li> <li> 21. iii Find the equation of the tangent to x 2 y 2 9 at the point 1, 2 2 x2 y 2 9 </li> <li> 22. iii Find the equation of the tangent to x 2 y 2 9 at the point 1, 2 2 x2 y 2 9 dy 2x 2 y 0 dx </li> <li> 23. iii Find the equation of the tangent to x 2 y 2 9 at the point 1, 2 2 x2 y 2 9 dy 2x 2 y 0 dx dy 2 y 2 x dx </li> <li> 24. iii Find the equation of the tangent to x 2 y 2 9 at the point 1, 2 2 x2 y 2 9 dy 2x 2 y 0 dx dy 2 y 2 x dx dy x dx y </li> <li> 25. iii Find the equation of the tangent to x 2 y 2 9 at the point 1, 2 2 x2 y 2 9 dy 2x 2 y 0 dx dy 2 y 2 x dx dy x dx y dy at 1, 2 2 , dx 1 2 2 </li> <li> 26. iii Find the equation of the tangent to x 2 y 2 9 at the point 1, 2 2 x2 y 2 9 dy 2x 2 y 0 dx dy 2 y 2 x dx dy x dx y dy at 1, 2 2 , dx 1 2 2 1 required slope 2 2 </li> <li> 27. iii Find the equation of the tangent to x 2 y 2 9 at the point 1, 2 2 x2 y 2 9 1 dy y2 2 x 1 2x 2 y 0 2 2 dx dy 2 y 2 x dx dy x dx y dy at 1, 2 2 , dx 1 2 2 1 required slope 2 2 </li> <li> 28. iii Find the equation of the tangent to x 2 y 2 9 at the point 1, 2 2 x2 y 2 9 1 dy y2 2 x 1 2x 2 y 0 2 2 dx 2 2y 8 x 1 dy 2 y 2 x dx dy x dx y dy at 1, 2 2 , dx 1 2 2 1 required slope 2 2 </li> <li> 29. iii Find the equation of the tangent to x 2 y 2 9 at the point 1, 2 2 x2 y 2 9 1 dy y2 2 x 1 2x 2 y 0 2 2 dx 2 2y 8 x 1 dy 2 y 2 x dx x 2 2y 9 0 dy x dx y dy at 1, 2 2 , dx 1 2 2 1 required slope 2 2 </li> <li> 30. iii Find the equation of the tangent to x 2 y 2 9 at the point 1, 2 2 x2 y 2 9 1 dy y2 2 x 1 2x 2 y 0 2 2 dx...</li></ul>