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Prove, Using the Rolle's theorem that be...

Prove, Using the Rolle's theorem that between any two distinct real zeros of the polynomial `a_(n) x^(n) + a_(n-1) x^(n-1) + …..a_(1)x + a_(0)` there is a zero of the polynomial .
`na_(n) x^(n-1) + (n-1) a_(n-1) x^(n-2) + ….+ a_(1)`

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PREMIERS PUBLISHERS-APPLICATIONS OF DIFFERENTIAL CALCULUS-Problems For Practice (Answer the following question)
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  2. The angular displacement theta radians of a fly wheel varies with time...

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  3. The distance s meters moved by a particle travelling in a straight lin...

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  4. A particle moves along a horizontal line such that its position at any...

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  5. A particle moves along a horizontal line such that its position at any...

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  6. A particle moves along a horizontal line such that its equation of mot...

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  7. A missile fixed from ground level raises x metres vertically upwards ...

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  8. A missile fixed from ground level raises x metres vertically upwards ...

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  9. A missile fixed from ground level raises x metres vertically upwards ...

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  10. A missile fixed from ground level raises x metres vertically upwards ...

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  11. A water tank has the shape of an invertd circular cone with base radiu...

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  12. At a particular instant ship A is 100 km west of ship B, ship A is sai...

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  13. A particle is fired straight up from the ground to each a height of x ...

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  14. Find the equation of tangent and normal to the curve y = x^(2) + 3x + ...

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  15. For what value of x the tangent of the curve y = x^(3) - 3x^(2) + 2x -...

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  16. Find the angle between the curves, (x^(2))/(8) + (y^(2))/(2) = 1 and (...

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  17. Find the equation of the tangent to the curve x^(2) + y^(2) = 5^(2) wh...

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  18. Find the equation of normal to y = x^(3) -3x that is parallel to 2x + ...

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  19. Verify Rolle's theorem for f(x) = sqrt(1 -x^(2)), -1 le x le 1

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  20. Using Rolle's theorem find the point on the curve y=x^(2)+1,-2lexle2 w...

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  21. Verify mean value theorem for the function f(x) = x^(3) - 5x^(2) 2x i...

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