Playing with math's Here we discuss some most imp.point JEE Notes | EduRev

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JEE : Playing with math's Here we discuss some most imp.point JEE Notes | EduRev

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1)if domain of a function is in closed interval then range is also must be in closed interval for continuous function but for discontinuous function it can be in open interval.
Eg.tanx
2)derivative of a differential function may or may not be continuous
Eg.X^2*sin(1/x) is a differential function but it's derivative have oscillatory type discontinuity 
3)if right hand derivative & left hand derivative both are finite but not equal then function still continuous with a sharp corner at that point,but not differentiable
4)for a homogeneous equation Dy/dx is always equal to y/x & D^2y/dx^2 is always equal to zero
5)if f(x) is continuous at x=a & g(x) is discontinues at x=a then f(x) g(x) is discontinues at x=a only when both function are define in ( a-$,a $)
Eg.f(x)=[x]is discontinues at x=2
   G(x)=√x-2 is continuous at x=2
    Then f(x) g(x)=[x] √x-2 is continuous at x=2


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