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Examine the continuity of the function f...

Examine the continuity of the function f defined by `f(x)`=`{[2x+1if x<1],[0 if x=1],[x^(2)-1 if x>1]:}`.

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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
  1. Find the value of k, so that the function defined by f(x)={(kx+1", if...

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

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  3. Examine the continuity of the function f defined by f(x)={[2x+1if x<1]...

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  4. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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  5. Find the relationship between a and b so that thefunction defined by f...

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  6. Find the value of a and b if the function given below is continuous. ...

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  7. For what value of k the following function is continuous at x=0 ? f(...

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  8. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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  9. Show that : sin^2x is continuous for everyreal value of x.

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

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  11. If 'f(x)= {((1-cos4x)/(x^2)),whenx<0),(k,whenx=0),(sqrtx/(sqrt(16+sqrt...

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  12. Find the value of k so that the function f defined by f(x)={((kcos x)/...

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  13. If the function f(x)={:{(3ax+b", if "xgt1),(11", if "x=1)...

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  14. Find all points of discontinuity of f, where f is defined by f(x)={:{(...

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  15. Find the derivative of tan^(-1)((cosx+sinx)/(cosx-sinx)) w.r.t. x.

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  16. What is the derivative of e^(3logx) w.r.t.x?

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  17. If u=t^2and v=sint^2then dv/du=.

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  18. If y=sec^(-1)(sqrtx+1)/sqrtx+sin^(-1)fracsqrtx(sqrtx+1)then dy/dx=

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  19. Write the derivative of sinx with respect to cosx.

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  20. If y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^(2))] then find (dy)/(dx)

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