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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.

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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-MODEL QUESTION PAPER 20-EXERCISE
  1. If A=[[0,-tan(alpha/2)],[tan(alpha/2),0]] show that (I+A) =(I-A)[[c...

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  2. Find the inverse of the matrix [[0,0,2],[0,2,0],[2,0,0]].

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

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  4. Find(dy)/(dx) when y=e^(x-y).

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  5. If y =2^(x^2)+ tan^(-1)2x then find (dy)/(dx).

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  6. Find dy/dx when siny=cos(x+y).

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  7. Find the intervals in which the function y=(lnx)/(x) is increasing and...

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  8. Integrate int e^x tan e^x dx.

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  9. Evaluate int (e^x-1)/(e^x+1) dx

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  10. Evaluate int(0)^(pi//4)log(1+tanx)dx.

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  11. Find the area of the region bounded by the curve y=6x-x^(2), the X-axi...

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  12. Solve(x log x )dy/dx+y=2 log x.

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  13. Show that the relation R defined on the set Z of all integers defined ...

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  14. If A = R -{3} and B = R -{1}. Consider the function f:A to B defined b...

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  15. Prove that 2 tan^-1(1/2) + tan^-1 (1/7) = tan^-1 (31/17).

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  16. Find the feasible region of the system. 2y-xge0,6y-3xle21,xge0,yge0

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  17. Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...

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  18. The diagonals of a parallelogram are given by veca =2hati - 3hatj + 5h...

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  19. Find the image of the point (2, 3, 4) with respect to the plane x - y ...

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  20. Find the equation of planes passing throught the points (1,2,3),(1,-4,...

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