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Show that the function defined by f(x)= ...

Show that the function defined by `f(x)= cos(x^(2))` is a continuous function.

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The correct Answer is:
`f(x) = cos (x^(2))`
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Exercise-5.1
  1. Find the values of k so that the function f is continuous at the indic...

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  2. Find the values of a and b such that the function defined by f(x)= {(5...

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  3. Show that the function defined by f(x)= cos(x^(2)) is a continuous fun...

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  4. Show that the function defined by f(x)= |cos x| is a continuous functi...

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  5. Examine that sin |x| is a continuous function.

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  6. Find all the points of discontinuity of f defined by f(x) = |x| - |x+1...

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  7. Prove that the function f(x)= 5x- 3 is continuous at x=0, at x= -3 and...

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  8. Examine the continuity of the function f(x)= 2x^(2) -1 " at " x=3

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  9. Examine the following functions for continuity. f(x)= x-5

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  10. Examine the following functions for continuity. f(x)= (1)/(x-5), x ...

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  11. Examine the following functions for continuity. f(x)= (x^(2)-25)/(x+...

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  12. Examine the following functions for continuity. f(x) = |x-5|

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  13. Prove that the function f(x)= x^(n) is continuous at x= n, where n is ...

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  14. Is the function f defined by f(x)= {(x",","if" x le 1),(5",","if" x gt...

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  15. f(x)= {(2x+3",","if" x le 2),(2x-3",","if" x gt 2):}

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  16. f(x)= {(|x|+3",","if" x le -3),(-2x",","if"-3 lt x lt 3),(6x + 2 ",","...

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  17. f(x) = {((|x|)/(x)",","if" x ne 0),(0",","if" x= 0):}

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  18. f(x)= {((x)/(|x|)",","if" x lt 0),(-1",","if" x ge 0):}

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  19. f(x)= {(x+1",","if" x ge 1),(x^(2) + 1",","if " x lt 1):}

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  20. f(x) = {(x^(3)-3",","if" x le 2),(x^(2)+1 ",","if " x gt 2):}

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