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Examine continuity and differentiability...

Examine continuity and differentiability `f(x)`=`{[xsin1/x,if x!=0],[0,ifx=0]:} `at `x=0`.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PROBLEM
  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. Examine the contiunity of the the following functions at indicated poi...

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  3. Examine continuity and differentiability f(x)={[xsin1/x,if x!=0],[0,if...

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  4. Test differentiability of the following function at the indicated poin...

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  5. Differentiate x^(sin^(-1)x w.r.t. sin ^(-1).

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  6. if x=e^(t)sin t and y=e^(t)cos t, then prove that (x+y)^(2)(d^(2)y)/dx...

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  7. Find dy/dx for (x+y)^(cosx) = e^(x+y).

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  8. If 2^(x)+2^(y)+2^(x+y) , then find dy/dx at x=y=1.

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  9. If y=x+e^(x),then find d^(2)x/dy^(2).

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  10. If e^(x)+e^(y)=e(x+y) find dy/dx.

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  11. Differntiate the following functions by proper substitution. [((1+t^2)...

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  12. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  13. Find dy/dx if log sqrt(x^2+y^2)=tan^(-1) (y/x)

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  14. sinx=2t/1+t^(2), tany=2t/1-t^(2), find dy/dx.

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  15. Find dy/dx, x=3 cos t-2cos^3t, y=3sint-2sin^3t.

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  16. If y=sin(mcos^(-1)x) then prove that (1-x^(2))y(2)-xy(1)+m^(2)y=0.

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  17. If y=cos^(-1)((2cosx-3sinx)/sqrt13), then find dy/dx.

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

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

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  20. Prove that e^x-2=0 has a solution between 0 and 1.

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