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Does there exists value of f(0) such tha...

Does there exists value of f(0) such that the following function becomes continuous at the origin `f(x)={x/(|x|), x!=0 `

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RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. Leg f(x+y)=f(x)+f(y)fora l lx , y in R , If f(x) is continue at x=0,...

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  2. Show that the function f(x) = |sinx+cosx| is continuous at x = p...

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  3. Does there exists value of f(0) such that the following function becom...

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

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

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

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

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

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

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

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

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

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  13. Discuss the differentiability of f(x)={x^2sin(1/x),\ \ \ \ x!=0; 0 i...

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

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

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

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

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

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  19. f(x)={|x-a|sin(1/(x-a)),\ \ \ for\ x!=a,\ \ \ 0\ \ \ if\ x=a at x=a

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  20. Show that f(x)={1+x^2, if 0<=x<=1, 2-x,\ \ \ if\ x >1 is discontinu...

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