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If f(x)={((x)/(e^(1/x)+1),",","when" x !...

If `f(x)={((x)/(e^(1/x)+1),",","when" x != 0),(0,",","when"x = 0):}`, then

A

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

B

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

C

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

D

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

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The correct Answer is:
C
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TARGET PUBLICATION-CONTINUITY-Critical Thinking
  1. The function f(x)=x^(2)"sin"(1)/(x), xne0,(f)0=0 at x=0

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  2. If f(x)={(x^(k) sin((1)/(x))",",x ne 0),(0",", x =0):} is continuous a...

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  3. If f(x)={((x)/(e^(1/x)+1),",","when" x != 0),(0,",","when"x = 0):}, th...

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  4. Which of the following functions is continuous at x = 0 ?

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  5. Let f(x)={(5^(1//x)"," , x lt 0),(lambda[x]",",x ge0):} and lambda in...

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  6. If f(x) = (x-a)/(sqrt(x)-sqrt(a)), x != a, is continuous at x = a then...

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  7. If f(x) = (sqrt(x+3)-2)/(x^(3)-1) , x != 1, is continuous at x = 1, th...

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  8. If f(x)={((sqrt(1+kx)-sqrt(1-kx))/(x),",","for" -1 lex lt 0),(2x^(2)+3...

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  9. If f(x) = {:((x^(4)-64x)/(sqrt(x^(2)+9)-5),",",x != 4),(k,",",x =4):} ...

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  10. If f(x) = (tan(x^(2)-x))/(x), x != 0, is continuous at x = 0, then f(0...

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  11. Function f(x) = (1-cos 4x)//(8x^(2)), " where " x != 0 , and f(x) = k...

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  12. Let f(x) = {((1-cos 4x)/(x^(2))",",x lt 0),(a",",x = 0),((sqrt(x))/(sq...

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  13. {:(f(x),=(1-cos 3x)/(x tan x),",","for" x != 0),(,=k, ",","for" x = 0)...

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  14. For what value of k, function f(x)={((k cosx)/(pi-2x)",","if "x ne (pi...

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  15. If {:(f(x),=(cos x - sin x)/(cos 2x),",", x != (pi)/4),(,=k, ",", x = ...

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  16. f:R->R is defined by f(x)={(cos3x-cosx)/(x^2), x!=0lambda, x=0 and f ...

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  17. If f(x) is continuous at x=pi/4, where f(x)=(1-tanx)/(1-sqrt(2)sin x),...

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  18. If f(x) ={((3sinx-sqrt(3)cosx)/(6x-pi),",",x != (pi)/6),(a, ",",x = pi...

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  19. If f(x)=(1-sinx)/((pi-2x)^2),w h e nx!=pi/2a n df(pi/2)=lambda, the f(...

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  20. If f(x) = ((a+x)^(2)sin(a+x)-a^(2)sin a)/(x) , x !=0, then the value o...

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