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The function f(x)=(1-cos x)/(x^(2))" for...

The function `f(x)=(1-cos x)/(x^(2))" for "x ne 0, f(0)=1" at x=0 is"`

A

continuous

B

discontinuous

C

not determined

D

none

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-LIMITS AND CONTINUITY-Exercise 1C(Continuity)
  1. The function f(x)=(x tan 2x)/(sin 3x sin 5x)" for "x ne 0, f(0)=2//17"...

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  2. The function f(x)=(cos 3x-cos 4x)/(x sin 2x)"for "x ne 0, f(0)=7//4"at...

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  3. The function f(x)=(1-cos x)/(x^(2))" for "x ne 0, f(0)=1" at x=0 is"

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  4. The function f(x)=(3sin x-sin 3x)/(x^(3))" for "x ne 0, f(0) =1 at x=0...

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  5. The function f(x)=(1-cos ax)/(1-cos bx)"for "x ne 0, f(0)=a/b" at x= 0...

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  6. The function f(x)=(sqrt(1+x^(2))-sqrt(1-x^(2))/(x^(2))"for "x ne 0, f(...

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  7. The function f(x) =(sqrt(x^(2)+3)-2)/(x-1)"for "x ne 1, f(1)=1//2" at ...

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  8. The function f(x) =(7|x|+5x)/(7|x|-5x) for x ne 0, f(0)=6" at x =0 is ...

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  9. If f(x)=1/(3^(1//x)+1)," then at x=0, f(x) is"

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  10. The function f(x) =[(x-1)/(1+e^(1/(x-1))]]" for "x ne 1, f(1)=0" ...

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  11. The function f(x) =(e^(1//x^(2))/(e^(1//x^(2))-1)" for "x ne 0,f(0)=1"...

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  12. f(x) = (x - [x]) sin ((1)/(X)) , at x = 0 , f is

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  13. If f(x)=x sin ""1/x"for "x ne 0, f(0)=0" then at x"=0, f(x) is

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  14. If f(x)=x cos""1/x^(2)" for "x ne 0, f(0)=1" then at x=0, f(x) is"

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  15. If f(x)=(x)/(1+e^(1//x))"for "x ne 0, f(0)=0" then at x=0, f(x) is"

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  16. The function f(x) =(xe^(1//x))/(1+e^(1//x))+sin""1/x" for "x ne 0, f(0...

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  17. If f(x)=(e^(1//x)-1)/(e^(1//x)+1)" for "x ne 0, f(0)=0" then at x=0, f...

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  18. If f(x)=(sin^(2)ax)/(x^(2))" for "x ne 0, f(0)=1 is continuous at x=0 ...

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  19. if f(x)=(1-cos ax)/(x sin x)" for "x ne 0, f(0)=1//2 is continuous at ...

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  20. A function f is defined by f(x)= {{:((sin (a + 1) x + sinx)/(x)" if...

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