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If {:(f(x),=(logx-log7)/(x-7),",",x != 7...

If `{:(f(x),=(logx-log7)/(x-7),",",x != 7),(,=k, ",",x = 7):}`
is continuous at `x = 7`, then the value of k is

A

`1/3`

B

`1/5`

C

`1/7`

D

`1/9`

Text Solution

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The correct Answer is:
C
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TARGET PUBLICATION-CONTINUITY-Critical Thinking
  1. If f(x) is continuous at x = (pi)/2, where f(x) = (sinx)^(1/(pi-2x)), ...

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  2. {:(f(x),=(log(1+kx))/(sin x),",",x != 0),(,=5, ",",x = 0):} If f is...

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  3. If {:(f(x),=(logx-log7)/(x-7),",",x != 7),(,=k, ",",x = 7):} is con...

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  4. If f(x) = {{:((log(1+2ax)-log(1-bx))/(x)",",x ne 0),(" "k",",...

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  5. {:(f(x),=((3^(sin x)-1)^(2))/(xlog(1+x)),",",x != 0),(,=k, ",",x = 0):...

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  6. The value of f(0) so that the function f(x) = (log(sec^2 x))/(x sin x)...

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  7. The value of a for which the function f(x)=f(x)={((4^x-1)hat3)/(sin(x...

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  8. f(x) ={((x^2-9)/(x-3)+a,",",x gt 3),(5, ",",x = 3),(2x^2+3x+b, ",",x l...

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  9. If f(x) is continuous at x = 0 , where f(x) ={(x^2+a,",",x ge 0),(2sqr...

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  10. Find the values of a and b sucht that the function f defined by ...

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  11. The value of p and q for which the function f(x) = {((sin(p+1)x+sinx...

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  12. If f(x) ={(e^(1/x),",","when"x != 0),(1,",","when"x = 0):} , then

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  13. If f(x) ={((x^(4)-16)/(x-2),",","when"x != 2),(16,",","when"x = 2):} ,...

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  14. The function f(x) = (|3x-4|)/(3x-4) is discontinuous at

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  15. If f(x) ={(|x|,",",x lt 0),(x,",",0 le x le 1),(1,",",x gt 1):} , the...

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  16. If {:(f(x),=(|x|)/(x),",","for" x != 0),(,=1, ",","for" x = 0):}, then...

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  17. The function (sinx)/(|x|)

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  18. If f(x) ={((x-|x|)/x,",","when"x != 0),(2,",","when"x = 0):} , then

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  19. Select the write the most appropriate answer from the given alternativ...

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  20. The function f(x)={{:(,(e^(1/x)-1)/(e^(1/x)+1),x ne 0),(,0,x=0):}

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