Home
Class 12
MATHS
Let f(x) = {{:(x^(2)/2", ...

Let ` f(x) = {{:(x^(2)/2", "0 lexlt1),(2x^(2)-3x+3/2", "1lexle2):}`
Discuss the continuity of f, f' and f'' on [0, 2].

Promotional Banner

Topper's Solved these Questions

  • Continuity, Differentiability and Graph of Function

    A DAS GUPTA|Exercise Exercise|38 Videos

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

  • Coordinates and Straight Lines

    A DAS GUPTA|Exercise EXERCISE|111 Videos

Similar Questions

Explore conceptually related problems

f(x)={(x^(2))/(2),0<=x<1 and 2x^(2)-3x+(3)/(2),1<=x<=2 Discuss the continuity of f,f; and f' on [0,2]

A function f(x) is defined by, f(x) = {{:(([x^(2)]-1)/(x^(2)-1)",","for",x^(2) ne 1),(0",","for",x^(2) = 1):} Discuss the continuity of f(x) at x = 1.

Find 'a' and 'b' if the function : f(x)={{:((sinx)/(x)" , "-2lexlt0),(a.2^(x)" , "0lexle1),(b+x", "1ltxle2):} is a continuous function on [-2, 2].

If f(x)={(x,,,0lexle1),(2-x,,,1ltxle2):} then point of discontinuity fo f(f(x)) is [0,2] is,

The function f(x) Is defined as follows : f(x)={{:(x^(2)+ax+b" , "0lexlt2),(3x+2" , "2lexle4),(2ax+5b" , "4ltxle8):} . If f(x) is continuous on [0,8], find the values of 'a' and 'b'.

If f(x) = {{:(x - 3",",x lt 0),(x^(2)-3x + 2",",x ge 0):}"and let" g(x) = f(|x|) + |f(x)| . Discuss the differentiability of g(x).

Given function f(x) ={:{(x^(2),"for " 0 lexlt1),(sqrt(x),"for "1 le x le2):}, "then" int_(0)^(2)f(x)dx is equal to

Discuss the continuity of the function f(x) given by f(x)={2x-1,quad if x =0

Discuss the continuity of the function f(x)={2x-1(3x)/2 ,ifx<2,ifxgeq2

A DAS GUPTA-Continuity, Differentiability and Graph of Function-Exercise
  1. Determine the values of a ,\ b ,\ c for which the function f(x)={(s...

    Text Solution

    |

  2. If g(x)=(1-a^x+x a^xloga)/(x^2*a^x), x<0 ((2a)^x-xlog(2a)-1)/(x^2), x...

    Text Solution

    |

  3. Let f(x) = {{:(x^(2)/2", "0 lexlt1),(2x^(2)-3x+3...

    Text Solution

    |

  4. Discuss the continuity of f(x)=(lim)(nvecoo)(x^(2n)-1)/(x^(2n)+1)

    Text Solution

    |

  5. The function f(x). defined as f(x)=lim(n->oo)(f(x)+x^(2n)g(x))/(1+x^(2...

    Text Solution

    |

  6. Consider the function f defines by f(x) = x-[x], where[x] denotes the ...

    Text Solution

    |

  7. The values of a and b so that the function f(x) = {{:(x + a sqrt(2) si...

    Text Solution

    |

  8. Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is contin...

    Text Solution

    |

  9. Leg f(x+y)=f(x)+f(y)fora l lx , y in R , If f(x)i scon t inuou sa tx=...

    Text Solution

    |

  10. Let f (x+y)=f (x) f(y) AA x, y in R , f (0)ne 0 If f (x) is continous ...

    Text Solution

    |

  11. Let f : [0, 1] rarr [0, 1] be a continuous function such that f (f (x)...

    Text Solution

    |

  12. The set of all points, where the function f (x) = x/(1+|x|) is dif...

    Text Solution

    |

  13. The set of points where ,f(x) = x|x| is twice differentiable is

    Text Solution

    |

  14. Let f(x) be difined in the interval [-2, 2] such that f(x)={{:(-1"...

    Text Solution

    |

  15. Let f(x) = {{:(x^(2)/2", "0 lexlt1),(2x^(2)-3x+3...

    Text Solution

    |

  16. Draw the graph of the function and discuss the continuity and differen...

    Text Solution

    |

  17. Given the function f(x) = 1/( 1-x) , The points of discontinuity of th...

    Text Solution

    |

  18. If f(x)={:{(ax^(2)-b", for " 0 le x lt1),(2", for " x=1),(x+1", for " ...

    Text Solution

    |

  19. If f(x)={(((1-sin^(3)x))/(3cos^(2)x)",",x lt (pi)/(2)),(a",",x=(pi)/(2...

    Text Solution

    |

  20. Let f(x)=( x^2+3x-10)/(x-2), x=!2. The value f(2) = will make the fun...

    Text Solution

    |