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Test the differentiability of the follow...

Test the differentiability of the following functions `f(x)=x/(1+absx)at x=0`.

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USHA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY APPLICATION OF DERIVATIVES -EXERCISE
  1. Find the derivative of the following functions from definition sqrt(ta...

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  2. f(x)={(x^2 sin (1/x), xne0 ),(0, x=0):} at x=0

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  3. Test the differentiability of the following functions f(x)=x/(1+absx)a...

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  4. If y = tan^-1((acosx-bsinx)/(bcosx+asinx)), then find (dy)/(dx)

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  5. If y = tan^-1(secx+tanx), then find (dy)/(dx).

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  6. Find (dy)/(dx), if y=sin^-1((sqrt(1+x)+sqrt(1-x))/2), -1ltxlt1

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  7. Find (dy)/(dx), if x=sqrt(sin2u) and y=sqrt(cos2u)

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  8. Find (dy)/(dx), if x=a(t-sint), y=a(1-cost)at t=(pi)/2

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  9. If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...

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  10. If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

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  11. Write the subinterval of (0,pi) in which sin (x+pi/4) is increasing.

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  12. Find the intervals where the following functions are (a) increasing an...

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  13. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

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  14. Find the points on the curve x^2+y^2-2x-4y+1=0,where the tangent is pa...

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  15. Find the equations of the tangent and the normal to the curve y = (x-7...

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  16. Find the angle of intersection of two curves y =2^x and y=5^x

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  17. Show that x/(1+ x tan x,) x in (0,pi/2)is maximum when x = cos x.

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  18. Show that f(x)=(logx)/xhas minimum value at x=e

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  19. Find (dy)/(dx) if x=(3at)/(1+t^3), y=(3at^2)/(1+t^3) at t=1/2

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  20. Find the extreme values of the function f(x)=x^2e^(-x^2) and show that...

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