Home
Class 11
MATHS
If f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):} ...

If `f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):}` ; `g(x)={(2x,,,xgt1),(3-x ,,,xle1):}` then the value of `lim_(x->1) f(g(x))` is

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If (x^2+x−2)/(x+3) -1) f(x) then find the value of lim_(x->-1) f(x)

If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt1),(x^(2)-2x-2",",1lexlt2),(x-5",",xge2):} Then the value of lim_(xrarr0) g(f(x))

If f(x)={{:(ax^(2)+1",",xgt1),(x+a",",xle1):} is derivable at x=1 , then the value of a is

If f(x)={(x^(2),xle1),(1-x,xgt1):} & composite function h(x)=|f(x)|+f(x+2) , then

if f(x) = {{:(x+2",",xle-1),(cx^(2)",",xgt-1):}, then find c when lim(xto-1)f(x) exists.

Let f(x)={(x+1,xle4),(2x+1,4ltxle9),(-x+7,xgt9):} and g(x)={(x^(2),-1lexlt3),(x+2,3lexle5):} then, find f(g(x)) .

If f(x)={{:(x^(2),xle0),(x,xgt0):} and g(x)=-absx,x inR, then find fog .

Let f(x) =e^(x-1)-ax^(2)+b and g(x)={{:(e^(x-1),xle1),(x^(2)+1,xgt1):}, then find the values of a and b such that f(x) xx g(x) is differentiable at x=1 .

If a function f:RtoR is defined by f(x){{:(2x,xgt3),(x^(2),1lexle3),(3x,xlt1):} Then the value of f(-1)+f(2)+f(4) is

If f(x)={{:(,ax^(2)-b,ale xlt 1),(,2,x=1),(,x+1,1 le xle2):} then the value of the pair (a,b) for which f(x) cannot be continuous at x=1, is

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. The reciprocal of the value of: ("lim")(nvecoo)(1-1/(2^2))(1-1/(3^2))(...

    Text Solution

    |

  2. Show that ("lim")(xrarr0) (e^(1/x)-1)/(e^(1/x)+1) does not exist

    Text Solution

    |

  3. If f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):} ; g(x)={(2x,,,xgt1),(3-x ,,,...

    Text Solution

    |

  4. Evaluate : ("lim")(xrarr2^+) ([x-2])/("log"(x-2)) , where [.] repres...

    Text Solution

    |

  5. The value of the limit ("lim")(xvec0)(a^(sqrt(x))-a^(1sqrt(x)))/(a^(sq...

    Text Solution

    |

  6. Evaluate: ("lim")(xrarr0) (sin[cosx])/(1+[cosx])([dot] denotes the g...

    Text Solution

    |

  7. lim(x->0)((1^x+2^x+...........+n^x)/n)^(1/x) is equal to

    Text Solution

    |

  8. Consider the following graph of the function y=f(x)dot Which of the fo...

    Text Solution

    |

  9. If lim(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

    Text Solution

    |

  10. If ("lim")(x->a)[f(x)+g(x)]=2a n d ("lim")(x->a)[f(x)-g(x)]=1, then f...

    Text Solution

    |

  11. Among (i) underset(xtooo)limsec^(-1)((x)/(sinx))" and "(ii) underset(x...

    Text Solution

    |

  12. Evaluate "lim"(x->0)(3x+|x|)/(7x-5|x|)

    Text Solution

    |

  13. The value of lim(x->0)(1+sinx-cosx+"log"(1-x))/(x^3) is 1/2 (b) -...

    Text Solution

    |

  14. lim(xvecoo)(e^(1/x^2)-1)/(2tan^-1(x^2)-pi) is equal to (a) 1 (b) -...

    Text Solution

    |

  15. Evaluate: lim(x->oo) (1+1/(a+bx))^(c+dx) , where a,b,c and dare positi...

    Text Solution

    |

  16. If x1=3 and x(n+1)=sqrt(2+xn),ngeq1,t h e n""("lim")(xrarroo)xn is (...

    Text Solution

    |

  17. Evaluate: ("lim")(xrarroo)(1+1/x)^x

    Text Solution

    |

  18. ("lim")(xvec0)("cos"(tanx)-cosx)/(x^4)i se q u a lto 1/6 (b) -1/3 (...

    Text Solution

    |

  19. Evaluate: ("lim")(xrarr0)((a^x+b^x+c^x)/3)^(2/x);(a , b , c >0)

    Text Solution

    |

  20. ("lim")(xvecoo)"{"x+5")"tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to ...

    Text Solution

    |