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Which of the following is not continuous...

Which of the following is not continuous for all x ?

A

`|x-1|+|x-2|`

B

`x^(2)-|x-x^(3)|`

C

`sin|x|+|sinx|`

D

`(cosx)/(|cosx|)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(cosx)/(|cosx|)` is not defined at `x=(2n+1)(pi)/(2), AA n in I`. Hence, discontinuous.
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-CONTINUITY-EXERCISE 2 (MISCELLANEOUS PROBLEMS)
  1. f(x)={(|x|+3",","if", x le -3),(-2x",", "if", -3 lt x lt 3),(6x+2",","...

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  2. The function f given by f(x)={((e^(1//x)-1)/(e^(1//x)+1)",","if",x ne...

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  3. Which of the following is not continuous for all x ?

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  4. Let f(x)=x^(3)+x be function and g(x)={(f(|x|)",", x ge 0),(f(-|x|)...

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  5. The value of f(0), so that the function f(x)=(1-cos(1-cosx))/(x^(4...

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  6. The jump value of the function at the point of the discontinuity of th...

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  7. f(x)=((4^x-1)^3)/(sin(x/p)log(1+(x^2)/3) is continuous at x=0 and f(0)...

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  8. If the function f(x)={(x+a^(2)sqrt(2)sinx",", 0 le x lt (pi)/(4)),(...

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  9. If f(x)={((sin 5x)/(x^(2)+2x)",", x ne 0),(k+(1)/(2)",", x =0):} is co...

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  10. If f(x) = 2x and g(x) = (x^(2))/(2)+1 , then which of the following ...

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  11. The function f(x) = (4-x^(2))/(4x-x^(3)) is

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  12. If f(x)={(x",", "if x is rational "),(-x",","if x is irrational"):}, ...

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  13. If f(x)={((cosx+3 sinx)^(5 "cosec"x)",",x in ((-pi)/(2),(pi)/(2))-{0}...

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  14. Let f(x)={( sqrt(1+x^(2))",", x lt sqrt(3)),(sqrt(3)x-1",", sqrt(3) le...

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  15. The value of f(0), so that the function f(x)=(sqrt(a^2-a x+x^2)-sqrt(...

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  16. The function f(x)=x-|x-x^(2)| is

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  17. For the function f(x)=(log(e)(1+x)+log(e)(1-x))/(x) to be continuous a...

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  18. The function f(x)=(1-sinx+cosx)/(1+sinx+cosx) is not defined at x=pi....

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  19. If f:R to R given by f(x)={(2cosx"," , "if", x le -(pi)/(2)),(a sin...

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  20. If the function f(x) ={((x^(2)-(k+2)x+2k)/(x-2),"for " x ne 2),(2," fo...

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