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Prove that the function f defined by f(x...

Prove that the function f defined by `f(x) = x^3 + x^2 -1` is a continuous function at x= 1.

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Prove that the following functions are continuous: sec x

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  2. Prove that the following functions are continuous: sin^-1x

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  3. Prove that the function f defined by f(x) = x^3 + x^2 -1 is a continuo...

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  4. Prove that the following functions are continuous: |x+1| +| x|

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  5. Prove that the following functions are continuous: sin |x|

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  6. Prove that the following functions are continuous: |sin x|

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  7. Prove that the following functions are continuous: |cos x|

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  8. Prove that the following functions are continuous: cosx^2

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  9. Show that the following functions are continuous: f(x) = sin(x^2)

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  10. Prove that the following functions are continuous: e^(cosx)

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  11. Prove that the following functions are continuous: e^x(tanx)

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  12. Prove that the following functions are continuous: (x^2 + x+1)/((x-1...

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  13. If f(x) = (|x-4|)/(4-x), x ne 4, f(4) = 0, show that f is continuous e...

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  14. Examine for continuity the following functions: f(x) = {:(x , if x n...

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  15. Examine for continuity the following functions: f(x) = {:(x/|x|, x n...

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  16. Examine for continuity the following functions: f(x) = {:(x^2, if x ...

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  17. Examine for continuity the following functions: f(x) = {:(2x-1, if x...

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  18. Examine for continuity the following functions: f(x) = {:{(sin x, if...

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  19. Examine for continuity the following functions: f(x) = {:{(x^2, if x...

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  20. Examine for continuity the following functions: f(x) = {:{(-2,if x l...

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