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A function `f(x)` is defined as `f(x)={(x^2-x-6)/(x-3);\ \ \ if\ x!=3\ \ \ \ \ \ 5;\ \ \ \ \ \ \ if\ x=3` Show that `f(x)` is continuous at `x=3` .

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To show that the function \( f(x) \) is continuous at \( x = 3 \), we need to verify that: \[ \lim_{x \to 3} f(x) = f(3) \] ### Step 1: Define the function ...
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RD SHARMA-CONTINUITY-Solved Examples And Exercises
  1. Show that thefunction f (x) = | sin x + cos x | is continuous at x =pi

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  2. Test the continuity of the following function at the origin: f(x)={...

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  3. A function f(x) is defined as f(x)={(x^2-x-6)/(x-3);\ \ \ if\ x!=3\ \ ...

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  4. A function f(x) is defined as f(x)={(x^2-9)/(x-3);\ \ \ if\ x!=3\ \ \ ...

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  5. If f(x)={(x^2-1)/(x-1);\ \ \ for\ x!=1\ \ \ 2;\ \ \ \ for\ x=1 . Find ...

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  6. If f(x)={(sin3x)/x ,\ \ \ w h e n\ x!=0 1,\ \ \ w h e n\ x=0 . Find wh...

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  7. If f(x)={e^(1//x),\ \ \ if\ x!=0 1,\ \ \ if\ x=0 . Find whether f is c...

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  8. Let f(x)={(1-cosx)/(x^2),\ \ \ w h e n\ x!=0 1,\ \ \ \ w h e n\ x=0 . ...

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  9. Show that f(x)={(x-|x|)/2,\ \ \ w h e n\ x!=0 2,\ \ \ w h e n\ x=0 is ...

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  10. Show that f(x)={(|x-a|)/(x-a),\ \ \ w h e n\ x!=a1,\ \ \ w h e n\ x=a ...

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  11. Discuss the continuity of f(x)={|x|cos(1/x),\ \ \ x!=0 0,\ \ \ \ x=...

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  12. Discuss the continuity of f(x)={x^2sin(1/x),\ \ \ \ x!=0\ \ \ \ \ \...

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  13. Discuss the continuity of f(x)={(x-a)sin(1/(x-a)),\ \ \ x!=a\ \ \ \...

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  14. f(x)={(e^x-1)/(log(1+2x)),\ \ \ if\ x!=0\ \ \ \ \ \ \ \ \ 7,\ \ \ \ \ ...

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  15. f(x)={(1-x^n)/(1-x),\ \ \ x!=1 ,\ \ \ n-1,\ \ \ x=1\ \ \ \ n in N a...

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  16. f(x)={(|x^2-1|)/(x-1),\ \ \ for\ x!=1 2,\ \ \ for\ x=1 at x=1

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  17. f(x)={(2|x|+x^2)/x ,\ \ \ x!=0 ,\ \ \ and 0 at x=0 is continuous at ...

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  18. f(x)={|x-a|sin(1/(x-a)),\ \ \ for\ x!=a0,\ \ \ for\ x=a at x=a

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  19. Show that f(x)={1+x^2,\ \ \ if\ 0lt=xlt=1 2-x ,\ \ \ if\ x >1 is disco...

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  20. Show that f(x)={(sin3x)/(tan2x),\ \ \ if\ x<0 3/2,\ \ \ if\ x=0(log(1+...

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