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Show that f(x) = {:{(5x-4, when, 0 lt x ...

Show that `f(x) = {:{(5x-4, when, 0 lt x le 1), (4x^(2) - 3x, when, 1 lt x lt 2):}` is continuous at `x = 1`.

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 9-Section C
  1. Show that f(x) = {:{(5x-4, when, 0 lt x le 1), (4x^(2) - 3x, when, 1 l...

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  2. If e^(x) + e^(y) = e^(x + y), then prove that (dy)/(dx) = (e^(x)(e^...

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  3. Find a point on the curve f(x)=(x-3)^2, where the tangent is parallel ...

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  4. Find the area of the region included between the parabolas y^(2) = 4ax...

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  5. Solve (dy)/(dx) = ysin 2x: y(0) = 1.

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  6. Evaluate int (1)/(sinx(2cos^(2) x -1)) dx.

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  7. Prove analytically : The perpendicular bisector of the sides of a tria...

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  8. Find the foot of the perpendicular drawn from the point 2hati - hatj +...

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  9. Solve the following LPP graphically. Maximise Z = 5x + 3y Su...

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  10. Let f : N to R be a function defined as f(x)=4x^(2)+12x +15. Show tha...

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  11. If A = [(1, -1, 1),(2, 1, -3), (1, 1, 1)], find A^(-1) and hence solve...

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  12. A dice is thrown thrice. Find the probability of getting an odd number...

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  13. Find the inverse of the following matrix using elementary transformati...

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  14. If e^(x) + e^(y) = e^(x + y), then prove that (dy)/(dx) = (e^(x)(e^...

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    |

  15. Find a point on the curve f(x)=(x-3)^2, where the tangent is parallel ...

    Text Solution

    |

  16. Find the area of the region included between the parabolas y^(2) = 4ax...

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    |

  17. Solve (dy)/(dx) = ysin 2x: y(0) = 1.

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    |

  18. Evaluate int (1)/(sinx(2cos^(2) x -1)) dx.

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  19. Prove analytically : The perpendicular bisector of the sides of a tria...

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    |

  20. Find the foot of the perpendicular drawn from the point 2hati - hatj +...

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    |

  21. Solve the following LPP graphically. Maximise Z = 5x + 3y Su...

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    |