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

The function `f(x)={(e^(1/x)-1)/(e^(1/x)+1),x!=0, at x=0 ,f(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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Verified by Experts

The correct Answer is:
`rArr" "underset(x rarr 0^(+))(lim)f(x) ne underset(x rarr 0^(-))(lim)f(x)`
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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  14. lf is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, th...

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  15. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

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  16. The left hand derivative of f(x) = [x] sin (pi x)"at x" = k is an inte...

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  17. Which of the following functions is differentiable at x = 0 ?

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  19. If the function g(X) ={{:( ksqrt ( x+1), 0 le x le 3),( mx+2, 3 lt x...

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