Home
Class 12
MATHS
If f(x)={x-1,xgeq 1 2x^2-2,x<1,g(x)={x...

If `f(x)={x-1,xgeq 1 2x^2-2,x<1,g(x)={x+1,x >0-x^2+1,xlt=0,a n dh(x)` `=|x|,t h e n lim_(x->0)f(g(h(x)))` is___

Text Solution

Verified by Experts

The correct Answer is:
`(0)`
`underset(xto0^(+))limf(g(h(x)))=f(g(0^(+)))=f(1^(+))=0`
`underset(xto0^(-))limf(g(h(x)))=f(g(0^(+)))=f(1^(+))=0`
Hence, `underset(xto0)limf(g(h(x)))=0`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise Archives JEE MAIN|8 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Archives JEE ADVANCED|2 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Matrix Match Type|5 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE PUBLICATION|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

f(x)={(x-1, -1lexlt0),(x^2, 0ltxle1):} and g(x)=sin x. Then find h(x)=f(|g(x)|)+|f(g(x))|

If f(x)=2/(x-3),g(x)=(x-3)/(x+4) , and h(x)=-(2(2x+1))/(x^2+x-12) then lim_(x->3)[f(x)+g(x)+h(x)] is (a) -2 (b) -1 (c) -2/7 (d) 0

f(x)={x ,xlt=0 1,x=0,t h e nfin d("lim")_(xvec0)f(x)x^2,x >0ife xi s t s

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

If f(x)={(x^nsin(1/(x^2)),x!=0), (0,x=0):} , (n in I) , then (a) lim_(xrarr0)f(x) exists for n >1 (b) lim_(xrarr0)f(x) exists for n<0 (c) lim_(xrarr0)f(x) does not exist for any value of n (d) lim_(xrarr0)f(x) cannot be determined

If f(x)={(-1, xlt0 ),(0, x =0),(1, x gt 0):} and g(x)=x(1-x^2), then , f(g(x)) is continuous for,

If f(x)={{:(x","" "xlt0),(1","" "x=0),(x^(2)","" "xgt0):}," then find " lim_(xto0) f(x)" if exists.

If f(x)=|x-2| a n d g(x)=f[f(x)],t h e n g^(prime)(x)= ______ for x>20

If f(x)=1/x ,g(x)=1/(x^2), and h(x)=x^2 , then (A) f(g(x))=x^2,x!=0,h(g(x))=1/(x^2) (B) h(g(x))=1/(x^2),x!=0,fog(x)=x^2 (C) fog(x)=x^2,x!=0,h(g(x))=(g(x))^2,x!=0 (D) none of these

CENGAGE PUBLICATION-LIMITS-Numerical Value Type
  1. The reciprocal of the value of: lim(n->oo)(1-1/(2^2))(1-1/(3^2))(1-1/(...

    Text Solution

    |

  2. lim(xtooo) f(x)," where "(2x-3)/(x)ltf(x)lt(2x^(2)+5x)/(x^(2))AAxgt0,"...

    Text Solution

    |

  3. If f(x)={x-1,xgeq 1 2x^2-2,x<1,g(x)={x+1,x >0-x^2+1,xlt=0,a n dh(x) ...

    Text Solution

    |

  4. If lim(x->oo) f(x) exists and is finite and nonzero and if lim(x->oo)...

    Text Solution

    |

  5. If L-("lim")(xvec2)((10-x)^(1/3)-2)/(x-2),t h e nt h ev a l u eof|1(4L...

    Text Solution

    |

  6. If lim(xto0) (p sin2x+(1-cos2x))/(x+tanx)=1, then the value of p is.

    Text Solution

    |

  7. The value of lim(xtooo) ((100)/(1-x^(100))-(50)/(1-x^(50))) is .

    Text Solution

    |

  8. If L= lim(xto2) (root(3)(60+x^(2))-4)/(sin(x-2)), then the value of 1/...

    Text Solution

    |

  9. The value of lim(xtooo) ((20^(x)-1)/(19(5^(x))))^(1//x) is .

    Text Solution

    |

  10. The value of lim(ntooo) [root(3)((n+1)^(2))-root(3)((n-1)^(2))] is .

    Text Solution

    |

  11. If L= lim(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^...

    Text Solution

    |

  12. The value of lim(x to oo ) (log(e)(log(e)x))/(e^(sqrt(x))) is . (a) π...

    Text Solution

    |

  13. Find k if x = 3 is a root of equation kx^2 – 10x + 3 = 0

    Text Solution

    |

  14. The value of lim(x to oo ) (x-x^(2)log(e)(1+(1)/(x))) is .

    Text Solution

    |

  15. Let Sn=1+2+3++n and Pn=(S2)/(S2-1)dot(S3)/(S3-1)dot(S4)/(S4-1)...(Sn)...

    Text Solution

    |

  16. If lim(xto1)(asin(x-1)+bcos(x-1)+4)/(x^(2)-1)=-2, then |a+b| is.

    Text Solution

    |

  17. Let lim(xto1) (x^(a)-ax+a-1)/((x-1)^(2))=f(a). Then the value of f(4) ...

    Text Solution

    |

  18. Number of integral values of k for which lim(xto1) sin^(-1)((k)/(log...

    Text Solution

    |

  19. If lim(xto1) (1+ax+bx^(2))^((c)/((x-1)))=e^(3), then find the value of...

    Text Solution

    |

  20. Let f ''(x) be continuous at x=0 If lim(xto0) (2f(x)-3af(2x)+bf(8x))...

    Text Solution

    |