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Evaluate lim(x to 0) (3X-2ln(1+X))/X....

Evaluate `lim_(x to 0) (3X-2ln(1+X))/X`.

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MODERN PUBLICATION-SAMPLE PAPER 2012-EXERCISE
  1. Differentiate a^(lnx) with respect to x.

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  2. Mention the values of x for which the frnction f(x) =x^(3) — 12x is in...

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  3. Evaluate lim(x to 0) (3X-2ln(1+X))/X.

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  4. What is F'(t) if F(t) = overset(t)underset(a)inte^(3x).cos2xdx?

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  5. integrate int(3+cosx+tan^2x)/(2x+sinx+tanx)

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  6. Write the particular solution of the equation dy/dx = sin x given that...

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  7. Write the order and degree of the following differential equation d^(2...

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  8. What is the point of intersection of the line x = y = z with the plane...

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  9. To which coordinate axis is the plane 2x+ 3z = 0 parallel ?

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  10. Find the component of the vector vec(b) = 8hat(i) + hat(j) in the dire...

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  11. What is the minimum value of n if P(n, 2) > 131 ?

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  12. What is the probability of getting a total of utmost 11 when two dice ...

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  13. Determine the maximum value of |[cosx sinx], [-sinx cosx-1]|.

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  14. Write the solution of the following LPP Maximise Z=x+y Subject to ...

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  15. Prove that , if y=logtan((pi)/(4)+(x)/(2)) , then (dy)/(dx)=secx

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  16. Differentiate with resi to x : Y = 2^(x^2) + tan^(-1)((cosx-sinx)/(cos...

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  17. Find del/(dely)((delz)/(delx)) if z=x^(y) + y^(x)

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  18. Evaluate lim(x to π/2) log(x-π/2)/tan x

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  19. Find the equation of tangent to the curve x=y^2-2 at the points where ...

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  20. Integrate int(-3//5)^(3//5)[2x+1]dx

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