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If the function `f(x) = {((cosx)^(1/x), ",", x != 1),(k, ",", x = 1):}` is continuous at x = 1, then the value of k is

A

1

B

`-1`

C

0

D

e

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The correct Answer is:
A
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TARGET PUBLICATION-CONTINUITY-Competitive Thinking
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  5. The function f(x) = (1-sin x + cos x)/(1+sin x + cosx) is not defined ...

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  6. If {:(f(x),=((e^(kx)-1)^(2)sinx)/(x^(3)),",",x != 0),(,=4, ",",x = 0):...

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  7. If f(x) = (e^(x^2)-cos x)/(x^(2)), "for" x != 0 is continuous at x = 0...

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

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  9. If {:(f(x),=log(1-3x)(1+3x),",",x != 0),(,=k, ",",x = 0):} is contin...

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  10. If {:(f(x),=(log)(sec^2x)^(cot^2x),",","for"x != 0),(,=k, ",","for"x =...

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  11. If the function {:(f(x),=[log((pi)/4+x)]^(1/x),",","for"x != 0),(,=k, ...

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  12. Function f(x) = {((log(2)2x)^(log(x)8), ",", x != 1),((k-1)^(3), ",", ...

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  13. For the function f(x) = (log(e )(1+x)-log(e )(1-x))/(x) to be continuo...

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  14. The function f(x) = (log(1+ax)-log(1-bx))/(x) is not defined at x = 0....

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  15. If the function f(x) = {((x^(2)-(A+2)x+A)/(x-2), ",", x != 2),(2, ",",...

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  16. The value of k which makes f(x) = {((sin(1/x)), ",", x != 0),(k, ","...

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  17. If the function f(x) defined by {:(f(x),=x (sin)1/x,",","for"x != 0)...

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  18. If f(x) = {(ax^(2)-b, ",", "when" 0 le x le 1),(2, ",","when"x = 1),(x...

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  19. If f(x) = {(sin x, ",", "if" x le 0),(x^(2)+a^(2), ",", "if" 0 lt x l...

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  20. If f(x) = {((1-sinzx)/(pi-2x), ",", x != pi/2),(lambda, ",", x = pi/2...

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