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If `f(x)` is continuous at `x=a,a>0`, where `f(x)=[(a^x-x^a)/(x^x-a^a)`, for `x!=a`, -1 for x=a, then `a=`

A

e

B

2e

C

1

D

0

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The correct Answer is:
C
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NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
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  2. If f(x) is continuous at x=pi/2, where f(x)=(3^(x- pi/2)-6^(x- pi/2))...

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  3. If f(x) is continuous at x=a,a>0, where f(x)=[(a^x-x^a)/(x^x-a^a), for...

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  4. If f(x) is continuous at x=0, where f(x)={:{((log (1+kx))/(sin x)", f...

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  5. For what value of k, the function defined by f(x)={((log(1+2x)sin x^...

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  6. If f(x) is continuous at x=0, where f(x)=(log sec^(2)x)/(x sin x), fo...

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  7. If f(x) is continuous at x=0, where f(x)=(log(1+x^(2))-log(1-x^(2)))/...

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  8. If f(x) is continuous at x=0, where f(x)=(log(1+x+x^(2))+log(1-x+x^(2...

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  9. If f(x) is continuous at x=0, where f(x)=(log(2+x)-log(2-x))/(tan x),...

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  10. If f(x) is continous at x=0, where f(x) ((e^(3x)-1)sin x)/(xlog(1+x)),...

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  11. If f(x)=((8^(x)-1)^(2))/(sin x log (1+ x/4)) in [-1, 1] - {0}, then f...

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  12. If f(x) is continuous at x=0, where f(x)=((4^(sin x)-1)^(2))/(x log (...

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  13. If f(x) is continuous at x=0, where f(x)=((3^(sin x)-1)^(2))/(x log (...

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  14. If f(x) is continuous at x=0, where f(x)={:{(((e^(x)-1)^(4))/(sin(x^(2...

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  15. If f(x)=(e^(x)+e^(-x)-2)/(x sin x), for x in [(-pi)/(2), (pi)/(2)]-{0}...

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  16. The function defined by f(x)={:{((1+tan^(2)sqrt(x))^((1)/(2x))", for "...

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  17. The function defined by f(x)={((x^(2)+e^((1)/(2-x)))^(-1)",",x ne 2)...

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  18. If f(x)=x^(2)-sin x+5, then at x=pi

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  19. If f(x)={:{(x", for " 0 le x lt 1/2),(1-x", for " 1/2 le x lt 1):} , t...

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  20. If f(x)={:{((x^(2)-9)/(x-3)", for " 0 lt x lt 3),(x+3", for " 3 le x l...

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