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Find the differentiable function which s...

Find the differentiable function which satisfies the equation `f(x)= -int_0^x f(t) tant dt + int_0^x tan(t-x)dt` where `x in (-pi/2,pi/2)`

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The correct Answer is:
cosx -1
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MOTION-DIFFERENTIAL EQUATION -Exercise 3
  1. Find the curve for which any tangent intersects the y-axis at the poin...

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  2. Find the curve such that the area of the trapezium formed by the co-or...

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  3. Find the equation of the curve passing through the origin if the middl...

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  4. A perpendicular drawn from any point P of the curve on the x-axis meet...

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  5. The equation of curve in which portion of y-axis cutoff between origin...

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  6. Find the orthogonal trajectories for the given family of curves when ‘...

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  7. The population P of a town decreases at a rate proportional to the num...

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  8. It is known that the decay rate of radium is directly proportional to ...

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  9. Let the function ln f(x) is defined where f(x) exists for x geq 2 an...

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  10. Find the differentiable function which satisfies the equation f(x)= -i...

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  11. Find all functions f(x) defined on (-pi/2,pi/2) with real values and h...

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  12. A tank contains 100 litres of fresh water. A solution containing 1 gm/...

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  13. A tank with a capacity of 1000 litres originally contains 100 gms of s...

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  14. (dy)/(dx)=y+int0^1 ydx given y=1 where x=0

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  15. Find the continuous function which satisfies the relation, int0^x t f(...

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  16. A curve passing through (1, 0) such that the ratio of the square of th...

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  17. The curve f(x) is given by

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  18. The curve g(x) is given by -

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  19. The value of int1^2(g(x) -f(x))dx is-

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  20. {:( " Column - I" , " Column - II") , ( "(A) A curve passing through...

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