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Show that the function f(x) = {:{(x^n si...

Show that the function `f(x) = {:{(x^n sin(1/x), x ne 0),(0, x = 0):}` is continuous but not differentiable at x= 0.

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find the derivative of following cot7x +3x^5 +sin3x

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  2. Let f(x) = (e^(1//x))/(1+e^(1//x)) for x ne 0. Find f (0) if f is left...

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  3. Show that the function f(x) = {:{(x^n sin(1/x), x ne 0),(0, x = 0):} i...

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  4. Find ainR so that f(x) = {:{(x^2, x ge0),(ax,x<0):} is continuous at 0...

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  5. Let f(x) = (2^(1/x))/(1+2^(1/x)) for x ne 0. Find f(0) if f is right c...

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  6. Let f(x) = [sinx], is f continuous at x = pi/2

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  7. Let f(x) = {:{(2x-5,if xge2),(x^2, if x <2):}. Is f continuous at x = ...

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  8. Determine the value of the constant k so that the function f(x) = {:{(...

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  9. Given f(x) = 1/(x+2). Write down the set of points of discontinuity of...

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  10. Write down the domain of continuity of the function f(x) = x|x|

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  11. Let f(x) = |x| cos (1/x) for x ne 0. Write the down the value of (f) ...

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  12. Write down the domain of continuity off(x) = e^(|x|)

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  13. Let f(x) = x[x]. Is f continuous on left of x = 2.

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  14. Find the value of 'k', such that the function : f(x) = {:{(2x^(x+2)-...

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  15. Find d/(dx)(1/(sqrt(1-x^2))

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  16. Compute d/(dx) (x|x|) when x < 0

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  17. Find dy/dx when xy = 1

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  18. Write down the value of dy/dx at x = e when y = log(a) x

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  19. Compute d/(dx)(sin^-1(sinx)) when pi/2 le x le (3pi)/2

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  20. Find d/(dx)(cos^-1 (cosx)) when pi le x le 2pi

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