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The function f(x)={{:(,(e^(1/x)-1)/(e^(1...

The function `f(x)={{:(,(e^(1/x)-1)/(e^(1/x)+1),x ne 0),(,0,x=0):}`

A

is continuous at x=0

B

is not continuous at x=0

C

is not continuous at x-0, but can be made continuous at x=0

D

None of these

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OBJECTIVE RD SHARMA-CONTINUITY AND DIFFERENTIABILITY-Exercise
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  2. If f(x)={{:(,(sqrt(x+1)-1)/(sqrtx),"for "x ne 0),(,k, for x=0):} and f...

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  3. The function f(x)={{:(,(e^(1/x)-1)/(e^(1/x)+1),x ne 0),(,0,x=0):}

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  4. Let f(x)={(x-4)/(|x-4|)+a ,x<4a+b ,(x-4)/(|x-4|)+b ,x >4 Then f(x) is...

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  5. If the function f(X)={{:(,(cos x)^(1//x),x ne 0),(,k,x=0):} is continu...

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  7. Let f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)|)\ \ \ \ ,\ \ \ x!=1,\ 1 6\ \ \ \ ...

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  9. If f(x)=[{:(mx+1,if x le (pi)/(2)),(sinx+n,ifxgt(pi)/(2)):} is contin...

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  11. The function f(x)={{:(,1,|x| gt1),(,(1)/(n^(2)),(1)/(n) lt |x| lt (1)/...

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  12. The value of f(0), so that the function f(x)=((27-2x)^2-3)/(9-3(243+5x...

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  13. The value of f(0) so that the function f(x)=(2-(256-7x)^(1/8))/((5x+32...

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  15. If f(x)=x sin ((1)/(x)),x ne 0 then the value of the function at x=0, ...

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  16. Let f(x)=[x] and g(x)={0, x in Z x^2, x in R -Z then (where [.]denot...

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  18. Let f(x) be a function differentiable at x=c. Then lim(x to c) f(x) e...

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  19. If lim(x to c) (f(x)-f(c))/(x-c) exists finitely, then

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  20. If f(x)={{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):} then

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