Home
Class 12
MATHS
f(x)={{:(3x-8, if x le 5),(2k, if x gt...

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

Text Solution

Verified by Experts

The correct Answer is:
N/a
We have, ` f(x)={{:(3x-8, if x le 5),(2k, if x gt 5) :}` at `x = 5`
Since , `f(x)` is continous at `x = 5`.
`:. LHL = RHL = f(5)`
Now, `LHL = underset(xrarr5^(-))(lim)(3x-8)=underset(hrarr0)(lim)[3(5-h)-8]`
`= underset(hrarr0)(lim)[15-3h-8]=7`
`RHL = underset(xrarr5^(+))(lim)2k = underset(hrarr0)(lim)2k=2k=7, [:' LHL = RHL]`
and ` f(5) = 3xx5-8 = 7`
`:. 2k = 7 rArr k = 7/2`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR|Exercise Application Of Integrals|68 Videos

  • DETERMINANTS

    NCERT EXEMPLAR|Exercise Determinants|58 Videos

Similar Questions

Explore conceptually related problems

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

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

Is the function f defined by f(x)={{:(x, if x le 1),(5, if x gt 1):} continuous at x = 0? At x = 2 ?

f(x)={{:(1+x, if x le 2),(5-x,ifx gt 2):} at x = 2 .

If f(x)={{:(x, if x le 1),(5, if x gt 1):} , then x=0,x=1,and x=2 is

f(x)={{:(x, if x le 1),(5, if x gt 1):} , then x=-1,x=0,and x=2 is

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

Given f(x) = {(3x-8" for " ,x le5),(7 " for " ,x gt 5):} What is the value of the function: (i) at x = 3 and (ii) at x = 7?

Show tha the function f (x) = {{:(1+x"," if x le 2 ,), ( 5-x "," if x gt 2):} is not differentiable at x = 2 .

Find 'k' so that : lim_(x to 2) f(x) exists, where : f(x)={{:(2x+3",", "if "x le 2), (x+2k",", "if "x gt 2):}

NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
  1. {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2, if l lt x le 2):} at x = ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. If f(x) = x^(2)sin'(1)/(x), where x ne 0, then the value of the functi...

    Text Solution

    |

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

    Text Solution

    |

  15. Show that f(x)=|x-3| is continuous but not differentiable at x=3 .

    Text Solution

    |

  16. A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all ...

    Text Solution

    |

  17. Differentiate 2^(cos^(2)x)

    Text Solution

    |

  18. Differentiate (8^(x))/(x^(8))

    Text Solution

    |

  19. Differentiate log(x+sqrt(a^2+x^2)) with respect to x :

    Text Solution

    |

  20. Differentiate log[log(logx^(5))]

    Text Solution

    |