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

If `f(x)={(sin3x)/x ,\ \ \ w h e n\ x!=0 1,\ \ \ w h e n\ x=0` . Find whether `f(x)` is continuous at `x=0` .

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To determine whether the function \( f(x) \) is continuous at \( x = 0 \), we need to check if the following condition holds: \[ \lim_{x \to 0} f(x) = f(0) \] ### Step 1: Identify the function The function is defined as follows: ...
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RD SHARMA-CONTINUITY-Solved Examples And Exercises
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  2. If f(x)={(x^2-1)/(x-1);\ \ \ for\ x!=1\ \ \ 2;\ \ \ \ for\ x=1 . Find ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Find the value of ' a^(prime) for which the function f defined by f(x)...

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  19. Examine the continuity of the function f(x)={3x-2,\ \ \ xlt=0x+1,\ ...

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  20. Discuss the continuity of the function f(x)={x ,\ \ \ x >0 1,\ \ \ ...

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