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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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FULL MARKS-APPLICATIONS OF DIFFERENTIAL CALCULUS -ADDITIONAL QUESTIONS SOLVED
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  2. A water tank has the shape of an invertd circular cone with base radiu...

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  3. A car A is travelling from west at 50 km/hr and car B is travelling to...

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  4. The distance x metres travelled by a vehicle in time t seconds after t...

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

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  6. Gravel is being duped from a conveyor belt at a rate of 30 ft^(3)//min...

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  7. Prove that the sum of the intercepts on the co-ordinate axes of any ta...

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

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  9. Prove that the curves 2x^(2)+4y^(2)=1 and 6x^(2)-12y^(2)=1 cut each ot...

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  10. Show that the equation of the normal to the curve x=a cos ^(3) theta, ...

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  11. If the curve y^(2) = x and xy = k are orthogonal then prove that 8k^(2...

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  12. Verify Rolle's theorem for the following f(x) = x^(3) -3x + 3 " in "...

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  13. Suppose that f(0) = -3, and f' (x) le 5 for all values of x how large ...

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

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  15. Find 'C' of Lagrange's mean value theorem for the function f(x)=2x^(3)...

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  16. Find 'C' of Lagrange's mean value theorem for the function f(x) =x^(3)...

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  17. The Taylor's series expension of f(x)=sin x "about" x=(pi)/(2) is obta...

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  18. Obatin the Maclaurin's series expansion for the following function . ...

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  19. Evaluate underset(x rarr (pi)/(2))(lim) (log sin x)/((pi - 2x)^(2))

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  20. Evaluate: underset (xrarr0) lim (cot x) ^(sin x)

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  21. underset (x rarr infty) lim(log x^(x))/(x)

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