Home
Class 12
MATHS
If f(x)=(2)/(x-3),g(x)=(x-3)/(x+4)," and...

If `f(x)=(2)/(x-3),g(x)=(x-3)/(x+4)," and "h(x)=-(2(2x+1))/(x^(2)+x-12)," then "lim_(xto3) [f(x)+g(x)+h(x)]" is "`

A

1

B

`oo`

C

`sqrt(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`f(x)+g(x)+h(x)=(x^(2)-4x+17-4x-2)/(x^(2)+x-12)`
`=(x^(2)-8x+15)/(x^(2)+x-12)=((x-3)(x-5))/((x-3)(x+4))`
`:. underset(xto3)lim[f(x)+g(x)+h(x)]=underset(xto3)lim((x-3)(x-5))/((x-3)(x+4))=-(2)/(7)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Exercise (Multiple)|18 Videos

  • LIMITS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.8|8 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

If f(x)=(2)/(x-3),g(x)=(x-3)/(x+4) and h(x)=-(2(2x+1))/(x^(2)+x-12), then find lim_(x rarr3)[f(x)+g(x)+h(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 rarr3)[f(x)+g(x)+h(x)] is (a) -2(b)-1 (c) -(2)/(7) (d) 0

If f(x)={(3x-1),x>=1,(2x+3),x =2} then lim_(x rarr2)f(g(x))=

If f(x)={{:(x-1", "xge1),(2x^(2)-2", "xlt1):},g(x)={{:(x+1", "xgt0),(-x^(2)+1", "xle0):}," and " h(x)=|x|," then "lim_(xto0) f(g(h(x)))" is" _______.

If f(x)=cot^(-1)((3x-x^(3))/(1-3x^(2))) and g(x)=cos^(-1)((1-x^(2))/(1+x^(2))) then lim_(x rarr a)(f(x)-f(a))/(g(x)-g(a))

If f(x)=4x-5,g(x)=x^(2) and h(x)=(1)/(x) , then f(g(h(x))) is :

If f (x) = cot ^(-1)((3x -x ^(3))/( 1- 3x ^(2)))and g (x) = cos ^(-1) ((1-x ^(2))/(1+x^(2))) then lim _(xtoa)(f(x) - f(a))/( g(x) -g (a)), 0 lt 1/2 is :

CENGAGE-LIMITS-Exercise (Single)
  1. lim(xto0^(+)) (sum(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x), where nin...

    Text Solution

    |

  2. lim(xtooo) (sin^(4)x-sin^(2)x+1)/(cos^(4)x-cos^(2)x+1)is equal to

    Text Solution

    |

  3. If f(x)=(2)/(x-3),g(x)=(x-3)/(x+4)," and "h(x)=-(2(2x+1))/(x^(2)+x-12)...

    Text Solution

    |

  4. The value of lim(xto pi) (1+cos^(3)x)/(sin^(2)x)" is "

    Text Solution

    |

  5. The value of lim(xto2) (sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)" is "

    Text Solution

    |

  6. The value of lim(xto2) (2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))" is "

    Text Solution

    |

  7. The value of lim(xto2) (((x^(3)-4x)/(x^(3)-8))^(-1)-((x+sqrt(2x))/(x-2...

    Text Solution

    |

  8. If lim(xto-2^(-)) (ae^(1//|x+2|)-1)/(2-e^(1//|x+2|))=lim(xto-2^(+)) si...

    Text Solution

    |

  9. lim(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^...

    Text Solution

    |

  10. The value of lim(xto(1)/(sqrt(2))) (x-cos(sin^(-1)x))/(1-tan(sin^(-1)x...

    Text Solution

    |

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

    Text Solution

    |

  12. lim(xtooo) ((x^(3))/(3x^(2)-4)-(x^(2))/(3x+2))" is equal to "

    Text Solution

    |

  13. lim(ntooo) (n(2n+1)^(2))/((n+2)(n^(2)+3n-1))" is equal to "

    Text Solution

    |

  14. lim(xtooo) ((2x+1)^(40)(4x+1)^(5))/((2x+3)^(45)) is equal to

    Text Solution

    |

  15. lim(xtooo) [sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)] is equal to

    Text Solution

    |

  16. lim(xtooo) (2+2x+sin2x)/((2x+sin2x)e^(sinx)) is equal to

    Text Solution

    |

  17. lim(xtooo) ((x+1)^(10)+(x+2)^(10)+...+(x+100)^(10))/(x^(10)+10^(10)) i...

    Text Solution

    |

  18. lim(xtooo) (2sqrt(x)+3root(3)(x)+4root(4)(x)+...+nroot(n)(x))/(sqrt((2...

    Text Solution

    |

  19. If lim(ntooo) (n.3^(n))/(n(x-2)^(n)+n.3^(n+1)-3^(n))=1/3, then the ran...

    Text Solution

    |

  20. lim(ntooo) n^(2)(x^(1//n)-x^(1//(n+1))),xgt0, is equal to

    Text Solution

    |