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overset(pi//2)underset(-pi//2)int |sin x...

`overset(pi//2)underset(-pi//2)int |sin x|dx` =

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UNITED BOOK HOUSE-SET 14-EXERCISE
  1. Evaluate:underset(xrarr0)lim log(1 + alphax)/(sin betax)

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  2. If y = logxtanx, find (dy)/(dx).

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  3. overset(pi//2)underset(-pi//2)int |sin x|dx =

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  4. Form the diffential equation of family of parabolas having vertex at t...

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  5. If f(x) = (x-1)e^x + 1, show that f(x) is positive for all positive va...

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  6. Using direction ratios show that the points (2,6,3),(1,2,7) and (3,10,...

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  7. Find the equation of the plane which passing through the point hati + ...

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  8. For three mutually exclusive events X,Y and Z it is given that P(x) = ...

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  9. A discrete random variable X has the following distribution: find a.

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  10. If xy = 1 + a^2 then show that, tan^(-1) [1/(a + x)]+tan^(-1) [1/(a+y)...

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

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  12. If y = f(x^2) and f'(x) = sqrt (3x^2+1), find [(dy)/(dx)](x=2)

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  13. If y= (tan^(-1)x)^2, then show that (1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(d...

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  14. Prove that, int(cos 5x + cos4x)/(1-2cos 3x)dx= -(1/2 sin2x + sinx)+c

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  15. Solve:(dy)/(dx)=(3x + 4y+1)/(-4x+2y-3)

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  16. Solve:(x^2-1)(dy)/(dx) + 2xy = 2/(x^2-1)

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  17. vec a = hati +hatj + hatk and vecb = -2hati +hatj +2hatk represent two...

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  18. Find the vector alpha which is perpendicular to both 4 hati + 5hatj -...

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  19. Show that: overset(1)underset(0)int (log(1+x)/(1+x^2))dx= pi/8 log 2.

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  20. Evaluate:underset(n rarr infty)lim 1/n[sin (pi/(2n)) +sin((2pi)/(2n))+...

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