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If {:(f(x),=(cos x - sin x)/(cos 2x),","...

If `{:(f(x),=(cos x - sin x)/(cos 2x),",", x != (pi)/4),(,=k, ",", x = (pi)/4):}` is continous at `x = (pi)/4`, then the value of k is

A

`sqrt(2)`

B

`1/(sqrt2)`

C

`2sqrt(2)`

D

`1/(2sqrt(2))`

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The correct Answer is:
B
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TARGET PUBLICATION-CONTINUITY-Critical Thinking
  1. {:(f(x),=(1-cos 3x)/(x tan x),",","for" x != 0),(,=k, ",","for" x = 0)...

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

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

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

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

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

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

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  9. If the function f(x)=(2-sqrt(x+4))/(sin2x)(x ne 0) is continuous at x ...

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  10. The value of f(0), so that the function f(x)=((27-2x)^2-3)/(9-3(243+5x...

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  11. If f(x) is continuous at x=pi/2, where f(x)=(sqrt(2)-sqrt(1+sin x))/(...

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  12. If f(x) = ((1+sinx)-sqrt(1-sinx))/(x) , x != 0, is continuous at x = 0...

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  13. If the function f(x) = (cos^(2)x - sin^(2)x-1)/(sqrt(x^(2)+1)-1), x !=...

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  14. The value of f at x =0 so that funcation f(x) = (2^(x) -2^(-x))/x , ...

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  15. If f(x)=(3^(x)+3^(-x)-2)/(x^(2)) for x ne 0 is continuous at x = 0, i...

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  16. If f(x) is continuous at x = 0, where {:(f(x),=(8^(x)-2^(x))/(k^(x)-1)...

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

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  18. If {:(f(x),=(e^(5x)-e^(2x))/(sin 3x),",",x != 0),(,=k/2, ",",x = 0):} ...

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  19. If f(x) = (e^(x)-e^(sinx))/(2(x sinx)) , x != 0 is continuous at x = 0...

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  20. In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, f...

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