Home
Class 12
MATHS
Determine the values of a so that the f...

Determine the values of a so that the funtion is continuous at x=1.
`f(x)=x^2+4` when `xle2`.
`=x^2+a^2`, when `xlt1`.

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos
  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

Determine the values of x for which the following functions fails to be continuous or differentiable f(x) = {((1-x), x lt 1), ((1-x)(2-x), 1lexle2 ), ((3-x), x gt 2):}

Find the cofficients a and b such that the following function f is continuous and differentiable at x=+-1: f(x)={{:((1)/(|x|)," when "|x|ge1),(ax^(2)+b," when " |x|lt1):}

A function f(x) is defined as follows : f(x)=-x," when "x lt0 =2," when "0 lex lt2 =4-x," when "x ge2 Draw the graph of the function and from the graph examine whether f(x) is continuous at x = 0 and x = 2 or not.

The value of f(0) so that the function f(x)=frac(2x-sin^-1x)(2x+tan^-1x is continuous at each point in its domain is equal to

Let f(x) ={{:((1-cos 4x)/(x^(2))",","when" x lt 0),(a",","when"x=0),((x)/(sqrt(16+sqrtx)-4)",","when" x gt0):} Determine the value of a, if possible, so that f(x) is continuous at x=0.

find the values of a and b , such that f(x) ={ax^2+1,xle1 and x^2+ax+b , x gt1 is differentiable at x=1

Show that Roll's theorem is not applicable to the following function in the interval 0 le x le 2 : f(x)={(" "2x" when " x le 1),(4-2x" when "x gt 1):}

A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):} Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

The points of discontiuties of the funtion f(x)= (x+2)/(2x^2 - x - 1) are:

If the following function f (x) is continuous at x = 0 , find k : f(x)={{:((1-cos2mx)/(2x^(2)),"when " xne0),(" " k,"when " x =0):}

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. let f(x)=x^3-x^2-3x-1 , g(x)=(x+1)aand h(x)=f(x)/g(x) where h is a rat...

    Text Solution

    |

  2. For which of the following functions f(0) exists such that f(x) is con...

    Text Solution

    |

  3. Determine the values of a so that the funtion is continuous at x=1. f...

    Text Solution

    |

  4. Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| fo...

    Text Solution

    |

  5. Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-...

    Text Solution

    |

  6. The function f:R→R satisfies f(x^2 ).f ′′ (x)=f ′ (x).f ′ (x^...

    Text Solution

    |

  7. The second derivative of a single valued function parametrically re...

    Text Solution

    |

  8. If lim(x→0) ​ (x^asin^b x)/(sin(x^c)), where a , b , c in ...

    Text Solution

    |

  9. (d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2)...

    Text Solution

    |

  10. If f(1)=3,f^(prime)(1)=2,f ^(' ')(1)=4,t h e n(f^(-1))^(' ')(3)= a. 1...

    Text Solution

    |

  11. If (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

    Text Solution

    |

  12. If R=([1+((dy)/(dx))^2]^(3//2))/((d^2y)/(dx2)) , thenR^(2//3) can be p...

    Text Solution

    |

  13. If x=t^2,y=t^3,t h e n(d^2y)/(dx^2) is (a)3/2 (b) 3/(4t) (c) 3/(2t) (...

    Text Solution

    |

  14. The function f(x)=(x^3)/8-sinpix+4 in [-4,4] does not take the value a...

    Text Solution

    |

  15. If f(x)={(|x|-3 when x < 1), and (|x-2|+a , when x >= 1) & g(x)={2...

    Text Solution

    |

  16. The number of points of discontinuity of f(x)=[2x]^(2)-{2x}^(2) (where...

    Text Solution

    |

  17. The number of points of discontinuity of g(x)=f(f(x)) where f(x) is ...

    Text Solution

    |

  18. Consider two function y=f(x) and y=g(x) defined as f(x)={{:(ax^(2)+b...

    Text Solution

    |

  19. If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is cont...

    Text Solution

    |

  20. Let f(x)=(lim)(n rarr oo)sum(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (...

    Text Solution

    |