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Find the value of k, if the functions ar...

Find the value of k, if the functions are continuous at the points given against them :
`{:(f(x)=(sqrt3-tan x)/(pi-3x)",","for" x nepi/3),(=k",","for" x=pi/3):}}at x=pi/3.`

A

`(-2)/(3)`

B

`2/3`

C

`(-4)/(3)`

D

`4/3`

Text Solution

Verified by Experts

The correct Answer is:
D
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NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
  1. If (x)=(1-sqrt3tanx)/(pi-6x),"for"x nepi/6 is continous at x=pi/6, "fi...

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  2. If f(x) is continuous at x=pi/4, where f(x)=(tan(pi/4 -x))/(cot 2x), f...

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  3. Find the value of k, if the functions are continuous at the points giv...

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

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

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  6. If f(x)={{:((1-sinx)/(pi-2x),,","xne(pi)/(2)),(lambda,,","x=(pi)/(2)):...

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

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  8. If f(x) is contiuous at x= pi/2, where f(x)=(cosec x - sin x)/(pi/2 -...

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

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  10. If f(x) is continuous at x=pi, where f(x)=(1- cos ( 7(x-pi)))/(5(x - ...

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  11. If f(x) is continuous at x=0, where f(x)=(1+2x)^(1/x)", for " x!=0, ...

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  12. If f(x) is continuous at x=0, where f(x)={:{((1+3x)^(1/x)", for " x !...

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  13. If f(x) is continuous at x=0, where f(x)=((4-3x)/(4))^(8/x)", for " x...

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  14. If f(x)= {:{((x^(2)-4)/(x-2)", for " x!=2),(5", for " x=2):}, then at ...

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  15. If f(x)={:{(root(3)((4x+1)/(1-4x))", for " x!=0),(e^(6)", for " x=0):}...

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  16. If f(x) is continuous at x=0, where f(x)=((4-3x)/(4+5x))^(1/x)", for ...

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  17. If f(x) is continuous at x=2, where f(x)=(x-1)^((1)/(2-x)), for x!=2, ...

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  18. If f(x) is continuous at x=0, where f(x)={:{((sec^(2)x)^(cot^(2)x)", ...

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  19. If f(x) is continuous at x=pi/4, where f(x)=(1+cos 2x)^(4sec 2x), for ...

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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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