Lagrange’s mean value theorem is also called as _____

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Question:
Lagrange’s mean value theorem is also called as _____

1.Euclid’s theorem

2.Rolle’s theorem

3.a special case of Rolle’s theorem

4.the mean value theorem

Posted Date:-2022-05-15 10:21:55

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  1. A bullet fired into a target loses half of its velocity after penetrating 2.5 cm. How much further will it penetrate?
  2. A curve passes through (1, 1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve is in the first quadrant and has its area equal to 2. What will be the equation of the curve?
  3. A motor car travelling at the rate of 40 km/hr is stopped by its brakes in 4 seconds. How long will it go from the point at which the brakes are first applied?
  4. A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds, respectively.What is the velocity of the particle in 3 seconds?
  5. A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds,respectively.What is the distance described by the particle in 3 seconds?
  6. A particle moving in a straight line with uniform acceleration has a velocity 10 cm/sec and 8 seconds later has a velocity 54 cm/sec. What will be the described by the particle during the 10th second of its motion?
  7. A particle moving in a straight line with uniform acceleration has a velocity 10 cm/sec and 8 seconds later has a velocity 54 cm/sec. What will be the value of space described?
  8. A particle moving in a straight line with uniform retardation described 7cm in 5th second and after some time comes to rest. If the particle describes 1/64 part of the total path during the last second of its motion, for how long was the particle in motion?
  9. Another form of Rolle’s theorem for the continuous condition is _____
  10. Another form of Rolle’s theorem for the differential condition is _____
  11. At which point does the normal to the hyperbola xy = 4 at (2, 2) intersects the hyperbola again?
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  13. Does Rolle’s theorem applicable if f(a) is not equal to f(b)?
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  15. Find s for the given planes 2x + 2y + sz + 2 = 0 and 3x + y + z – 2 = 0, if they are perpendicular to each other.
  16. Find the angle between 2x + 3y – 2z + 4 = 0 and 4x + 3y + 2z + 2 = 0.
  17. Find the angle between the planes 5x + y + 3z + 1 = 0 and x + y – 2z + 6 = 0.
  18. Find the angle between x + 2y + 7z + 2 = 0 and 4x + 4y + z + 2 = 0.
  19. Find the area of the triangle with the vertices (2,3), (4,1), (5,0).
  20. Find the equation of the line joining A(2,1) and B(6,3) using determinants.
  21. Find the equation of the line joining A(5,1), B(4,0) using determinants.
  22. Find the value of k for which (1,2), (3,0), (2,k) are collinear.
  23. Find the value of k for which the points (3,2), (1,2), (5,k) are collinear.
  24. Function f is differentiable on [a,b] to satisfy Lagrange’s mean value theorem.
  25. Function f is differential on (a,b) according to Rolle’s theorem.
  26. Function f is not continuous on [a,b] to satisfy Lagrange’s mean value theorem.
  27. Function f should be _____ on [a,b] according to Rolle’s theorem.
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  30. In what ratio is the line segment joining the points A(-5, 2) and B(3, 9) divided by the x-axis?
  31. In what ratio is the line segment joining the points A(2, 4) and B(6, 5) divided by the y-axis?
  32. Lagrange’s mean value theorem is also called as _____
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