Home
Class 12
MATHS
Find ainR so that f(x) = {:{(x^2, x ge0)...

Find a`in`R so that `f(x) = {:{(x^2, x ge0),(ax,x<0):}` is continuous at 0.

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|788 Videos

  • APPLICATIONS OF INTEGRALS

    PRADEEP PUBLICATION|Exercise EXERCISE|162 Videos

  • DETERMINANTS

    PRADEEP PUBLICATION|Exercise EXERCISE|342 Videos

Similar Questions

Explore conceptually related problems

Show that the function 'f' given by: f(x) = {:{(x,if x ge1),(x^2,ifx<1):} is continous every where on R.

Find k, so that f(x) = {{:((sin kx)/(x)"," ,x != 0),(4+ x",", x = 0):} is continous at x = 0

Determine the value of the constant k so that the function f(x) = {:{(2x^2 + k, if x ge0), (-2x^2 + 4, if x < 0):} is continuous at x = 0

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):}

Examine for continuity the following functions: f(x) = {:{(sin x, if x < 0),(x, if x ge0):}

Find the values of a so that the function f defined by f(X) = {:{((sin^2ax)/x^2, x ne 0),(1, x = 0):} may be continuous at x = 0.

Examine the function for continuity at x = 0: f(x) = {:{(sinx/x, when x <0),(x+1,when x ge0):}

Discuss the continuity of the function f(x) at x = 2, where f(x) = {:{(3x + 5, if, x ge2),(x^2, if , x<2):}

Find k in R if f(x) = {:{((cos^2 x - sin^2 x -1)/(sqrt(x^2+1) - 1), x ne 0), (k, x = 0):} is continuous at 0.

PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Fill in the blanks: An example of a function which is continuous eve...

    Text Solution

    |

  2. If f(x)={(ax+1" if "xge1),(x+2" if "xlt1):} is continuous, then 'a' sh...

    Text Solution

    |

  3. Find ainR so that f(x) = {:{(x^2, x ge0),(ax,x<0):} is continuous at 0...

    Text Solution

    |

  4. Fill in the blanks: For all x in (6,7), d/(dx) ([x]) = ……………. .

    Text Solution

    |

  5. Fill in the blanks: Derivative of sin x w.r.t cos x is …………… .

    Text Solution

    |

  6. Fill in the blanks: Derivative of x^2 wr.t x^3 is …………… .

    Text Solution

    |

  7. Fill in the blanks: If xge0, then d/(Dx) {cos^-1((1-x^2)/(1+x^2))} i...

    Text Solution

    |

  8. The derivative of sin x cos x w.r.t. x is

    Text Solution

    |

  9. Fill in the blanks: The derivative of log(10) x w.r.t x is …………….. ...

    Text Solution

    |

  10. Fill in the blanks: If f(x) = |sin x|, then f'(pi/4) is equal to ………...

    Text Solution

    |

  11. Fill in the blanks: Domain of continuity of the function f(x) =|x-1|...

    Text Solution

    |

  12. Fill in the blanks: An example of a function which is continuous eve...

    Text Solution

    |

  13. Fill in the blanks: For the curve sqrtx + sqrty = 1, dy/dx at (1/4, ...

    Text Solution

    |

  14. Fill in the blanks: If f(x) = x^(2//3), then f'(0) is ……… .

    Text Solution

    |

  15. Fill in the blanks: Rolle's Theorem is not applicable to the functio...

    Text Solution

    |

  16. Every continuous function is differentiable.

    Text Solution

    |

  17. True or False : d/(dx) (logx) = 1/x for all x ne 0.

    Text Solution

    |

  18. True or False : d/(dx) (log|x|) = 1/x for all x ne 0

    Text Solution

    |

  19. If f is continuous on its domain D, then |f| is also continuous on D.

    Text Solution

    |

  20. True or False : Rolle's Theorem is applicable to the function f(x) =...

    Text Solution

    |