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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

`lim_(x to 0^(+))f(x) = -1`

B

f(x) is continuous at` x = 0`

C

`lim_(x to 0^(-))f(x) = 1`

D

f(x) is not continuous at` x = 0`

Text Solution

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The correct Answer is:
D
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TARGET PUBLICATION-CONTINUITY-Critical Thinking
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  7. If f(x) ={(4-3x,",",0 lt x le 2),(2x-6,",",2 lt x le 3),(x+5,",",3 lt ...

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  9. If f(y)={(((e^(2y)-1)*siny)/(y^(2)),", for "y ne 0),(4,", for "y=0):}...

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  10. For the function f(x)={((sin^(2)ax)/(x^(2))",","where " x ne 0),(1",",...

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  11. The points of discontinuity of tan x are

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  12. If f(x)={:{((sin 2x)/(sqrt(1-cos 2x))", for " 0 lt x lt pi/2),((cos x)...

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  16. If f(x) {:( =((2^(x)-1)^(2))/(sin x.log(1+x))", if " x != 0 ),(= ...

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  17. If f(x) = (tan(pi/4-x))/(cot2x), x != pi/4, is continuous in (0, pi/2)...

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  18. If f(x)={((sqrt(1+px)-sqrt(1-px))/(x) ",", -1 le x lt 0),((2x+1)/(x-2...

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