Home
Class 12
MATHS
Determine the constants 'a' and 'b' so t...

Determine the constants 'a' and 'b' so that the function 'f' defined below is continuous everywhere:
`f(x) = {:{(x+2,xle2),(ax+b,2 < x<5),(3x-2,xge5):}`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise EXERCISE|211 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

Similar Questions

Explore conceptually related problems

Determine the constants 'a' and 'b' so that the function 'f' defined below is continuous everywhere: f(x) = {(5,if, xle2) (ax+b,if, 2 (21,if,xge10)

Determine the constant k(if it exists), so that the following functions may be continuous: f(x) = {:{(kx^2, xle2),(3,x>2):}

In the following, determine the constant so that given function is continuous at indicated point: f(x) ={:{(kx^2, if x le2),(2,ifx>2):} at x =2

Determine the constant k(if it exists), so that the following functions may be continuous: f(x) = {:{(k(x^2 - 2x), x < 0),(cos x, x ge0):}

Determine the constant lambda , so that the function is continuous at x=1 f(x) = {{:((x -1)/(x + 1)"," , " if " x != 1),(lambda - 1",", "if "x = 1):}

In the following, determine the constant so that given function is continuous at indicated point: f(x) ={:{(kx+5,whenxle2),(x-1),whenx>2):} at x =2

Determine the constant k, so that function f (x) is continuous at the indicated points : f(x)= {((x^2-3x+2)/(x-1),if,x,ne,1),(k,if,x,=,1):} at x=1.

Show that the function defined by f(x) = cos(x^2) is a continuous function.

MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If the following function f(x) is continuous at x = 0, find the value ...

    Text Solution

    |

  2. Determine the constants 'a' and 'b' so that the function 'f' defined b...

    Text Solution

    |

  3. Determine the constants 'a' and 'b' so that the function 'f' defined b...

    Text Solution

    |

  4. If the function f(x) given by: f(x) = {:{(2ax+b,ifx>1),(9,ifx=1),(6a...

    Text Solution

    |

  5. Find the values of a and b so that the following function is continuou...

    Text Solution

    |

  6. Find 'a' and 'b' if the function: f(x) = {:{((sinx)/x, -2lex<0),(a.2...

    Text Solution

    |

  7. Find the values of 'p' and 'q' for which: f(x) = {:{((1-sin^3x)/(3co...

    Text Solution

    |

  8. The funtion f(x) is defined as follows: f(x) = {:{(x^2+ax+b,0lex<2),...

    Text Solution

    |

  9. A man is driving a car on the dangerous path given by: f(x) = {:{((1...

    Text Solution

    |

  10. Find all the points of discontinuity of the function f defined by f(x)...

    Text Solution

    |

  11. Find all points of discontinuity of f, where f is defined by : f(x)={(...

    Text Solution

    |

  12. Find all the points of discontinuity of f, where f is defined by f(x...

    Text Solution

    |

  13. Show that the following functions are continuous: f(x) = sin(x^2)

    Text Solution

    |

  14. Show that the following functions are continuous: f(x) = cos(x^2)

    Text Solution

    |

  15. Show that the following functions are continuous: f(x) = |cosx|

    Text Solution

    |

  16. Show that the function 'f' given by: f(x) = |x| + |x-1|, x in R is c...

    Text Solution

    |

  17. Show that the function 'f' given by: f(x) = |x-1|+|x-2|, x in R is c...

    Text Solution

    |

  18. Locate the points of discontinuity of the function: f(x) = {:{((x^4-...

    Text Solution

    |

  19. Examine the derivability of the following functions at the specified p...

    Text Solution

    |

  20. Examine the derivability of the following functions at the specified p...

    Text Solution

    |