Home
Class 12
MATHS
If f(x)={(ax^2+b ,0lex<1),(4,x=1),(x+3,...

If `f(x)={(ax^2+b ,0lex<1),(4,x=1),(x+3,1ltxge2))` then the value of`(a ,b)` for which `f(x)` cannot be continuous at `x=1,` is (a)`(2,2)` (b) `(3,1)`(c)`(4,0)` (d)`(5,2)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos

  • DEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|562 Videos

Similar Questions

Explore conceptually related problems

Evaluate the left-and right-hand limits of the function defined by f(x)={(1+x^2, 0lex<1), (2-x ,x gt1):} at x=1 Also, show that lim_(xrarr1)f(x) does not exist

If f(x)={{:(,ax^(2)-b,|x|lt 1),(,(1)/(|x|),|x| ge1):} is differentiable at x=1, then

Find the values of a and b so that the function f(x) defined by f(x)={(x^2 +ax+b),(0<=x<2),(3x+2) , (2<=x<=4), (2a x+5b), (4 < x <= 8)} becomes continuous on [0,pi].

If f(x)=ax^2 + bx + c , a ne 0 and a, b , and c are all negative , which could be the graph of f(x) ?

Find the value of 'a' and 'b' lim_(x to 2) and lim_(x to 4) exists where f(x){{:(x^(2)+ax+b,0lexlt2),(3x+2,2lexle4),(2ax+5b,4ltxle8):}

If f(x)={{:(1+x",",-1lexlt0),(x^(2)-1",",0ltxlt2),(2x",",2lex):} Find f(3),f(-2),f(0),f((1)/(2))f(2-h),f(-1+h) , where hgt0 is very small.

Let f (x) =ax ^(2) +bx + c,a ne 0, such the f (-1-x)=f (-1+ x) AA x in R. Also given that f (x) =0 has no real roots and 4a + b gt 0. Let p =b-4a, q=2a +b, then pq is:

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

let f(x) = {:{( x^(2) , x le 0) , ( ax , x gt 0):} then f (x) is derivable at x = 0 if

Let f(x) be defined in the interval [0,4] such that f(x) ={{:(1-x,0lex le 1),( x+2, 1lt xlt2),( 4-x, 2 le x le 4):} , then the number of points where f(x) is discontinuous is (a) 1 (b) 2 (c) 3 (d) none of these

RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. Discuss the continuity of the function f(x) given by f(x)={2x-1,ifx...

    Text Solution

    |

  2. The value of a for which the function f(x)={(((4^x-1)^3)/(sin(x/a)log...

    Text Solution

    |

  3. If f(x)={(ax^2+b ,0lex<1),(4,x=1),(x+3,1ltxge2)) then the value of(a...

    Text Solution

    |

  4. If f(x)={(2^(x+2)-16)/(4^x-16), if x!=2, k if x=2 is continuous at x=2...

    Text Solution

    |

  5. Let f(x)={(1-cos4x)/(x^2a,),ifx<0(sqrt(x))/(sqrt(16+sqrt(x))-4),ifx >0...

    Text Solution

    |

  6. if the function f(x) defined by f(x)=(log(1+a x)-"log"(1-b x))/x ,...

    Text Solution

    |

  7. Find the value of a if the function f(x) defined by f(x)={2x-a, ,x<...

    Text Solution

    |

  8. Find the value of the constant k so that the function given belo...

    Text Solution

    |

  9. Discuss the continuity of the f(x) at the indicated point: f(x)=...

    Text Solution

    |

  10. 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

    |

  11. If f(x)=(sqrt(2)cosx-1)/(cotx-1),x!=pi/4dot Find the value of f(pi/4) ...

    Text Solution

    |

  12. Determine f(0) so that the function f(x) defined by f(x)=((4^x-1)^3)/...

    Text Solution

    |

  13. The function f(x)={x^2a a,if1lt=x<sqrt(2),if0lt=1(2b^2-4b)/(x^2),ifsqr...

    Text Solution

    |

  14. Iff(x)={(x-4)/(|x-4|)+a,ifx<4 a+b,if x = 4 (x-4)/(|x-4|)+b,if x >4 is ...

    Text Solution

    |

  15. Prove that the function f(x)={x/(|x|+2x^2),x!=0 and k ,x=0 remains d...

    Text Solution

    |

  16. Show that f(x)={((sin3x)/(tan2x) ,, if x<0),(3/2 ,, if x=0),((log(1+3...

    Text Solution

    |

  17. Find all point of discountinuity of the function f(t) = (1)/(t^(2)...

    Text Solution

    |

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

    Text Solution

    |

  19. If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then (...

    Text Solution

    |

  20. Let f(x)=(log(1+x/a)-log(1-x/b))/x ,x!=0. Find the value of f at x=0...

    Text Solution

    |