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Determine if f defined by f(x)={{:(x s...

Determine if f defined by
`f(x)={{:(x sin""(1)/(x)," if "x ne 0),(0," if "x= 0):}` is a continuous function?

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The correct Answer is:
yes, f is continuous for all `x in R`.
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NCERT TAMIL-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.1
  1. Find the relationship between a and b so that the function f defined b...

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

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

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  4. Is the function defined by f(x)= x^(2)-sin x+5 continuous at x= pi?

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  5. Discuss the continuity of the following functions : f(x)= sin x +cos...

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  6. Discuss the continuity of the following functions : f(x)= sin x - co...

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  7. Discuss the continuity of the following functions : f(x) = sin x. co...

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  8. Discuss the continuity of the cosine, cosecant, secant and cotangent f...

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  9. Find all points of dicontinuity of f, where f(x)={{:((sinx)/(x)," if...

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  10. Determine if f defined by f(x)={{:(x sin""(1)/(x)," if "x ne 0),(0,"...

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  11. Examine the continuity of f, where f is defined by f(x)={{:(sin x-co...

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

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

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

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

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

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

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

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

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

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