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Rolle's theorem is applicable in the int...

Rolle's theorem is applicable in the interval [-2,] for the function

A

`f(x)=x^(3)`

B

`f(x)=4x^(4)`

C

`f(x)=2x^(3)+3`

D

`f(x)=pi|x|`

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Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example? f(x)= [x]" for "x in [-2, 2] .

Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example? f(x) = x^(2)-1 " for "x in [1, 2] .

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Examine whether Rolle's theorem is applicable to the following function in the given intervals: f(x) = cos x in - pi/2 le x le pi/2

Show that Rolle's theorem is not applicable to the following functions in the specified intervals: f(x)=2+(x-2)^((2)/(3))" in " 1 le x le 3

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WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2012-MULTIPLE CHOICE QUESTIONS
  1. lim(x to 0) (pi^(x)-1)/(sqrt(1+x)-1)

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  2. If f is a real- valued differentiable function such that f(x)f'(x) lt ...

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  3. Rolle's theorem is applicable in the interval [-2,] for the function

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  4. The solution of 25(d^(2)y)/(dx^(2))-10(dy)/(dx)+y=0, y(0)=1, y(1)=2e^(...

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  5. Let P be the midpoint of a chord joining the vertex of the parabola y^...

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  6. The line x=2y intersects the ellipse (x^(2))/(4)+y^(2)=1 at the points...

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  7. The eccentric angle in the first quadrant of a point on the ellipse (x...

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  8. The transverse axis of hyperbola is along the x-axis and its length is...

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  9. A point moves in such a way that the difference of its distance from t...

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  10. The number of integer values of m, for which the x-coordinates of the ...

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  11. If a straight line passes through the point (alpha, beta) and the port...

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  12. The coefficient of x^(10) in the expansion of 1+(1+x)+...+(1+x)^(20) i...

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  13. Examine the consistency of the system of equations x+ y +z=1 2x+...

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  14. Let A and B be two events with P(A^(C))=-0.3, P(B)=0.4 and )P(A nn B^(...

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  15. Let p,q,r be the altitudes of a triangle with area S and perimeter 2t....

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  16. Let C(1) and C(2) denote the centres of the circles x^(2)+y^(2)=4 and ...

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  17. A straight line through the point of intersection of the lines x+2y+4=...

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  18. Let P and Q be the points on the parabola y^(2)=4x so that the lines ...

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  19. The incentre of an equilateral triangle is (1,1) and the equation of o...

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  20. The value of lim(x to oo) ((n!)^((1)/(n)))/(n) is

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