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Show that the function f(x) = {{:(x^2 + ...

Show that the function `f(x) = {{:(x^2 + 3 , "if" x != 0),(1,"if" x = 0):}` is not continous at `x = 0`.

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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES (Short Answer Type Questions)(Section II)
  1. Prove that the function f(x) = 5x-3, is contNuous at x=0, at x=-3 a...

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  2. Prove that the function f(x) = x + |x| is continuous at x = 0.

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

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  4. Discuss the continuity of function f(x) at 0 , if f(x) = |x| .

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  5. Discuss the continuity of f(x) = 0 at x = 0 if f(x) = {{:((sqrt(1 + ...

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  6. Show that the function f(x) = {{:(x^2 + 3 , "if" x != 0),(1,"if" x = 0...

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  7. Determine the constant k, so that function f (x) is continuous at the ...

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  8. Determine, k if the following function is continuous at x = 0 f(x) =...

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  9. Find the values of k so that the function f is continuous at the indic...

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  10. Find the value of k so that the function f is continuous at the indica...

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  11. Find the relationship between a and b so that the function f defined b...

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  12. For what value of lambda is the function defined by f(x)={(lambda(x^2...

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

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  14. Is the function defined by f(x)={(x+5,,,,if x le 1),(x-5,,,,if x>1):}...

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  15. Determine if f defined by : f(x)={(x^2sin(1/x),,,, if x ne0),(0,,,, if...

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

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