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Let f (x)= {{:( xe ^(ax)"," , x le 0),( ...

Let `f (x)= {{:( xe ^(ax)"," , x le 0),( x+ ax ^(2)-x ^(3)"," , x gt 0):}` Where a is a positive constnat . The interval in which f '(x) is increasing is `[(k)/(a ),(a)/(l)],` Then `k +l` is equal to

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VK JAISWAL-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. On [1,e], then least and greatest vlaues of f (x) = x^(2)ln x are m a...

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  2. If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...

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  3. Let f (x)= {{:( xe ^(ax)"," , x le 0),( x+ ax ^(2)-x ^(3)"," , x gt 0)...

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  4. Find sum of all possible values of the real parameter 'b' is the diffe...

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  5. Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...

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  6. Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...

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  7. Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...

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  8. There is a point (p,q) on the graph of f(x)=x^2 and a point (r , s) on...

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  9. f (x)= max |2 sin y-x| where y in R then determine the minimum value o...

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  10. Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...

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  11. The numbr of real roots of the equation x ^(2013)+ e ^(20144x) =0 is

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  12. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

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  13. The least positive integral value of 'k' for which there exists at lea...

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  14. Let f (x) =x ^(2) +2x -t ^(2) and f(x)=0 has two root alpha (t ) and b...

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

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  16. If f (x) is continous and differentiable in [3,9) and f'(x) in [-2,8] ...

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  17. It is given that f 9x) is difined on R satisfyinf f (1)=1 and for AA ...

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  18. The number of normals to the curve 3y ^(3) =4x which passes through th...

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  19. Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...

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  20. Let f (x) = ax+cos 2x +sin x+ cos x is defined for AA x in R and a in...

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