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f(x)={{:(3x+5, if x ge 2),(x^(3), if x...

`f(x)={{:(3x+5, if x ge 2),(x^(3), if x le 2):}`at `x = 2`

A

`f(x)` is discontinuous at `x = 2`.

B

`f(x)` is continuous at `x = 2`.

C

Can not be determined

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `f(x)={{:(3x+5, if x ge 2),(x^(3), if x le 2):}`at `x = 2`
At `x = 2 LHL = underset(xrarr2^(-))(lim)(x)^(2)`
`= underset(hrarr0)(lim)(2-h)^(2)=underset(hrarr0)lim(4+h^(2)-4h)=4`
and `RHL = underset(xrarr2^(+))(lim)(3x+5)`
`= underset(hrarr0)(lim)[3(2+h)+5]=11`
Since, ` LHL ne RHL` at `x= 2`
So, `f(x)` is dicontinuous at `x = 2`.
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NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
  1. Examine continuity of the function f(x) = x^(3) + 2x^(2)- 1 at x = 1...

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  2. f(x)={{:(3x+5, if x ge 2),(x^(3), if x le 2):}at x = 2

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  3. f(x)={{:((1-cos2x)/(x^(2)),if x ne 0),(5, if x = 0):} at x = 0.

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  4. f(x) = {{:((2x^(2)-3x-2)/(x-2), if x ne 2), (5, if x = 2):} at x = 2.

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  5. f(x)= {{:((|x-4|)/(2(x-4)), if x ne 4),(0,if x = 4):} at x = 4.

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  6. f(x)={{:(|x|cos'1/x, if x ne 0),(0, if x =0):} at x = 0 .

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  7. Find that the function is continuous or discontinuous at the indicated...

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  8. f(x)={{:(e^(1//x)/(1+e^(1//x)),if x ne 0),(0,if x = 0):}at x = 0

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  9. {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2, if l lt x le 2):} at x = ...

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  10. f(x) = |x| + |x-1| at x = 1.

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  11. f(x)={{:(3x-8, if x le 5),(2k, if x gt 5) :} at x = 5

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  12. f(x) ={{:((2^(x+2)-16)/(4^(x)-16), if x ne 2 ),(k, if x = 2):} ,x = 2.

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  13. f(x) = {{:((sqrt(1+kx)-sqrt(1-kx))/(x),if -1 le x lt 0),((2x+1)/(x-1...

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  14. The value of k for which the function defined as f(x) = {{:((1-coskx)...

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  15. Prove that the function f defined by f(x) = {{:((x)/(|x|+2x^(2)), if ...

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

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  17. Given the function f(x)=1/(x+2) . Find the points of discontinuity of...

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  18. Find all point of discontinuity of the function f(t)=1/(t^2+t-2), wher...

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  19. Show that the function f(x)=|sinx+cosx| is continuous at x=pi .

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  20. Examine the differentiability of f, where f is defined by f(x) = {{:(...

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