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Select the write the most appropriate answer from the given alternatives in each of the following :
The function `f(x)=(|x|)/(x^(2)+2x), x ne 0and f(0)=0` is not continuous at `x=0` because

A

`lim_(x to 0)f(x) != f(0)`

B

`lim_(x to 0^(+))f(x)` does not exist

C

`lim_(x to 0^(-))f(x)` does not exist

D

`lim_(x to 0)f(x)` does not exist

Text Solution

Verified by Experts

The correct Answer is:
D
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TARGET PUBLICATION-CONTINUITY-Critical Thinking
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  2. If f(x) ={((x-|x|)/x,",","when"x != 0),(2,",","when"x = 0):} , then

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  3. Select the write the most appropriate answer from the given alternativ...

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

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  5. f(x) = (x^(2)+x-2)/(x^(2)-3x+2) is discontinuous at x =

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  6. The point at which the function f(x) = (x+1)/(x^(2)+x-12) is discontin...

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  7. The function f(x) = (4-x^(2))/(4x-x^(3)) is

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  8. 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(x)={:{(x sin x", for " 0 lt x le pi/2),(pi/2 sin (pi+x)", for " p...

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

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

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  12. The points of discontinuity of tan x are

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

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  14. If {:(f(x),=(x cos x - 3tan x)/(x^(2)+2sinx),",",x != 0),(,=1, ",",x =...

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  15. If f(x) ={((5^(x)-e^(x))/(sin 2x),",",x != 0),(1/2(log 5+1),",",x = 0)...

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  16. f(x)={((5^(cosx)-1)/((pi)/(2)-x)",", x ne (pi)/(2)), (log 5"," , x =(p...

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

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

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

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  20. The function f(x) = (x^(2)-4)/(sin x-2) is

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