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Show that f(x)={(sin3x)/(tan2x),\ \ \ if...

Show that `f(x)={(sin3x)/(tan2x),\ \ \ if\ x<0,\ 3/2,\ \ \ if\ x=0,\(log(1+3x))/(e^(2x)-1),\ \ \ if\ x >0` is continuous at `x=0`

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RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. f(x)={|x-a|sin(1/(x-a)),\ \ \ for\ x!=a,\ \ \ 0\ \ \ if\ x=a at x=a

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

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  3. Show that f(x)={(sin3x)/(tan2x),\ \ \ if\ x<0,\ 3/2,\ \ \ if\ x=0,\(lo...

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

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

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

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  7. Discuss the continuity of the function f(x)={(x , 0 le x lt1/2 ),( 1...

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  8. Discuss the continuity of f(x)={2x-1,\ \ \ x<0 ; {2x+1,\ \ \ xgeq0 a...

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  9. For what value of k is the function f(x)={(x^2-1)/(x-1),\ \ \ x!=1k ,\...

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  10. Determine the value of the constant k so that the function f(x)={(x^...

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  11. For what value of k is the function f(x)={(sin5x)/(3x),\ \ \ if\ x!=0,...

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  12. Determine the value of the constant k so that the function f(x)={k ...

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  13. Determine the value of the constant k so that the function f(x)={(si...

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  14. Find the values of a so that the function f(x)={a x+5,\ \ \ if\ xlt=2 ...

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  15. Prove that the function f(x)={x/(|x|+2x^2),\ \ \ x!=0k ,\ \ \ x=0 r...

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  16. Find the value of k if f(x) is continuous at x=pi//2 , where f(x)={(kc...

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  17. Determine the values of a ,\ b ,\ c for which the function f(x)={(si...

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  18. If f(x)={(1-cosk x)/(xsinx),x!=0 \ \ \ \ \ \ \ \ 1/2,x=0 is continuo...

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  19. If f(x)={(x-4)/(|x-4|)+a ,\ \ \ if\ x<4, a+b \ \ \ if\ x=4, (x-4...

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  20. For what value of k is the function f(x)={(sin2x)/x ,\ \ \ x!=0k ,\ \ ...

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