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Verify Rolle's theorem for the function ...

Verify Rolle's theorem for the function f(x) = sin x + cosx in the interval `ole x le pi//2`

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UNITED BOOK HOUSE-SET 19-EXERCISE
  1. Prove that (a+b+c+x) is a factor of |(x+a, b,c),(b,x+c,a),(c,a,x+b)|

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  2. If P = ((1,2,1),(1,3,1)) and Q = PP^T , then find Q

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  3. Verify Rolle's theorem for the function f(x) = sin x + cosx in the int...

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  4. Evaluate : underset(x rarr0) Lt (logecosx)/(sin^2 x)

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  5. Evaluate: int((cosx+xsinx)/(x(x+cosx)))dx.

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  6. If x>1/2, show that the function f(x) = x(4x^2 - 3) is steadily increa...

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  7. If |veca| = sqrt3,|vecb| = 2 and veca.vecb = sqrt6, then find the angl...

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  8. If the line (x-2)/(6) = (y-1)/(lambda) = (z+5)/(-4) is perpendicular t...

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  9. The probability that A hits a target is 1/3 and the probability that B...

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  10. An unbiased coin is toosed 7 times. Find the probability of getting an...

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  11. answer any one question : (ii) prove that , tan(pi/4 +1/2 (cos ^(-1) (...

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  12. Solve : |(x+4, 2x,2x),(2x , x+4, 2x),(2x, 2x, x+4)| = 0

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  13. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

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  14. If y^(1/3) + y^(-1/3) = 2x, prove that (x^2 - 1)y2 + xy1 = 9y.

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  15. Evaluate : int(loge(x+1))/((x+1)^2) dx

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  16. Evaluate :int(5^(5^(5^x)cdot 5^(5^(x))cdot 5^x))dx

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  17. Solve the differential equation: (1+y^2)+(x - e^(tan^-1 y) )dy/dx = 0

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  18. Find the unit vector which is perpendicular to both veca = 2hati + 3ha...

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  19. If veca = hati + hatj + hatk , vecb = hatj - hatk then find a vector v...

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  20. Evaluate: underset(nrarralpha)Lt[1/(sqrt(2n-1^2)) +1/(sqrt(4n-2^2))+1/...

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