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Examine the continuity of the following ...

Examine the continuity of the following functions at the indicated points: `f(x) = {(x+1/2,xle1/2),(3/2-x a,xgt1/2):}at x=1/2`

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USHA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY APPLICATION OF DERIVATIVES -EXERCISE
  1. Find the extreme points of the function y= x+1/x.

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  2. Does the. normal at any point on a circle passes through the centre of...

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  3. Examine the continuity of the following functions at the indicated poi...

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  4. examine the contiunity of the following functions at indicated points ...

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  5. Examine the contiunity of the following functions at the indicated poi...

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  6. Examine the continuity of the following functions at indicated points....

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  7. Examine the contiunity of the the following functions at indicated poi...

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  8. Find the derivative of the following functions from definition sqrtx c...

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  9. Find the derivative of the following functions from definition sin^2x.

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  10. Find the derivative of the following functions from definition sqrt(ta...

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

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

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

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

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

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

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

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

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

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

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