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

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

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Test differentiability and continuity of the following functions. f(x) = {(x sin (1/x), x ne 0), (0, x = 0) :} at x = 0.

Show that f(x)={(x sin frac{1}{x}, xne0),(o,x=0):} is continuous at x=0

Examine the continuity of the function f(x)={{:((|sinx|)/(x)", "x!=0),(1", "x=0):} at x=0

Show that f(x)={(xsinfrac{1}{x},xne0),(0,x=0):} is not differentiable x=0

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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
  1. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. if e^x+e^y=e^(x+y) then show that (dy)/(dx)+e^(y-x)=0.

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  15. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

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  16. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

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  17. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) w.r.t sin^(-1)((2x)/(1+x^2))...

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  18. Write that condition of Rolle’s theorem which is violated by the funct...

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  19. If f(0)=0,f'(0)=2 then what is the derivative of y = f(f(f(f(x)))) at...

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  20. If y = tan^(-1)(1/(1+x+x^2)) + tan^(-1)(1/(x^2+3x+3)) + tan^(-1)(1/(x^...

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