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f(x) = {(3x-8,",", "if"x le 5),(2k,",", ...

`f(x) = {(3x-8,",", "if"x le 5),(2k,",", "if"x gt 5):}` is continuous at x = 5, find k.

A

`4/7`

B

`2/7`

C

`7/2`

D

`3/7`

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The correct Answer is:
C
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TARGET PUBLICATION-CONTINUITY-Competitive Thinking
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  2. The function 'f' is defined by f(x) = 2x - 1, if x gt 2, f(x) = k if ...

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  4. If {:(f(x),=x^(2)+alpha,",","for"x ge 0),(,=2sqrt(x^(2)+1)+beta, ",","...

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

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  6. If f(x) = {((x^(2)+3x-10)/(x^(2)+2x-15),",", "when"x != -5),(a,",", "w...

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  7. If f(x) = {((x^(2)-9)/(x-3),",", "if"x != 3),(2x+k,",", "otherwise"):}...

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  8. If f(x) = {((sqrt(1+kx)-sqrt(1-kx))/(x), "if" -1 le x lt 0),((2x+k)/(x...

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  9. If f(x) = {((sin 2x)/(5x), ",", "when" x != 0),(k, ",", "when" x = 0...

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  10. If f(x) = {((3sin pix)/(5x), ",",x != 0),(2k, ",",x = 0):} is continu...

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  11. If f(x) = |x-2|, then

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  12. If f(x) = |x-b|, then the function

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  13. If f(x) = {(1, ",", "when" 0 lt x le (3pi)/4),(2(sin) 2/9x, ",", "when...

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  14. If f(x) = {((1-cosx)/x, ",", x != 0),(k, ",", x = 0):} is continuous a...

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  15. If the function f(x) = {((cosx)^(1/x), ",", x != 1),(k, ",", x = 1):} ...

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  16. If f(x) = {((log(e )x)/(x-1), ",", x != 1),(k, ",", x = 1):} is contin...

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  17. The function f(x) = (1-sin x + cos x)/(1+sin x + cosx) is not defined ...

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

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

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

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