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If f(x)={{:((sinpix)/(5x)",",x ne0),(k,"...

If `f(x)={{:((sinpix)/(5x)",",x ne0),(k,","0):}` is continuous at x=0 , then k is equal to

A

`(5)/(pi)`

B

`(pi)/(5)`

C

1

D

0

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The correct Answer is:
B
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ICSE-CONTINUITY AND DIFFERENTIABILITY -MULTIPLE CHOICE QUESTIONS
  1. If f(x){{:((sqrt(4+x)-2)/(x)",",xne0),(k,","x=0):} is continuous at x...

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  2. If f(x)={{:((sqrt(x^(2)+5)-3)/(x+2)",",x ne-2),(k,","x=-2):} is conti...

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  3. If f(x)={{:((sinpix)/(5x)",",x ne0),(k,","0):} is continuous at x=0 ,...

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  4. The value of the function f at x=0 so that the function f(x)=(2^(x)-2...

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  5. If f(x)=(2x+sin^(-1)x)/(2x-tan^(-1)x) is continuous for all x in (-1,1...

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  6. If f(x)={{:((1-tanx)/(4x-pi)",",x ne(pi)/(4)),(k ",",x=(pi)/(4)):} is...

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  7. If f(x)={{:(tan((pi)/(4)-x)/(cot2x)",",x ne(pi)/(4)),(k",",x=(pi)/(4))...

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  8. If f(x)={{:((1-cospx)/(xsinx)",",x ne0),((1)/(2)",",x=0):} is continu...

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  9. If f(x)={{:((sqrt(1-cos2x))/(sqrt(2)x)",",xne0),(k",",x=0):} then whi...

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  10. If f(x)={{:(x^(2)"sin"(1)/(x)",",x ne0),(k",",x=0):}

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  11. If f(x)={{:(mx+1",",xle(pi)/(2)),(sinx+n",",xge (pi)/(2)):} is contin...

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  12. The function f(x) =|x| at x=0 is

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  13. The function f(x) = x |x| at x= 0 is

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  14. The derivative of the function f(x) =x|x| at x= 0 is

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  15. If f(x)={{:(x",",0lexle1),(x+a",",xgt1):} then

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  16. If f(x)={{:(ax^(2)+1",",xgt1),(x+a",",xle1):} is derivable at x=1 , t...

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  17. The function f(x)=|x|+|x-1| is

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  18. The derivative of f(x)=3|2+x| at x=-3 is

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  19. The derivative of f(x)=|x-1|+|x-3| at x=2 is

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  20. The function f(x) =e^(|x|) is

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