Home
Class 11
MATHS
If f(x)=2/(x-3),g(x)=(x-3)/(x+4) , and h...

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`

A

1

B

`oo`

C

`sqrt(2)`

D

none of these

Text Solution

Verified by Experts

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

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If f(x)=sinx, g(x)=x^2 and h(x)=log x, find h[g{f(x)}].

If f(x) = e^(x + a) , g(x) = x^(b^2) and h(x) = e^(b^2 x) , then find the value of (g{f(x)})/(h(x))

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)) is equal to-

If f(x)=3x+1,g(x)=x^3+2 , then (f+g)/(fg) (0) =?

If f(x)=(1)/(x^2) , show that f(x+h)-f(x-h)=-(4xh)/((x^2-h^2)^2) .

If f(x) is defined on [2,2] by f(x) = 4x^2-3x+1 and g(x) = (f(-x)-f(x))/(x^2+3) then int_(-2)^2g(x) dx is equal to

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-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+2)^3]| then coefficient of x in f(x) is (a) -4 (b) -2 (c) -6 (d) 0

Prove that lim_(x->0) (f(x+h)+f(x-h)-2f(x))/h^2 = f''(x)

If f(x)=tan^(-1)((3x-x^(3))/(1-3x^(2))) and phi(x)=cos^(-1)((1-x^(2))/(1+x^(2))) , then the value of lim_(x to a) (f(x)-f(a))/(phi(x)-phi(a))(0 lt a lt (1)/(2)) is -

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. lim(x->0)(x(e^x-1))/(1-cosx) is equal to

    Text Solution

    |

  2. Evaluate: lim(x->oo)[x(a^(1/x)-1)], a >1

    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) then...

    Text Solution

    |

  4. Evaluate: lim(xto0) ((1-3^(x)-4^(x)+12^(x)))/(sqrt((2cosx+7))-3)

    Text Solution

    |

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

    Text Solution

    |

  6. Evaluate: lim(x->0)(a^(tanx)-a^(sinx))/(tanx-sinx),a >0

    Text Solution

    |

  7. lim(x->oo)((2x+1)^(40)(4x-1)^5)/((2x+3)^(45)) is equal to (a)16 ...

    Text Solution

    |

  8. Evaluate: lim(x->a)("log"(x-a))/(log(e^x-e^a))

    Text Solution

    |

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

    Text Solution

    |

  10. Evaluate: lim(x->0)(e^x+e^(-x)-2)/(x^2)

    Text Solution

    |

  11. lim(n->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x ...

    Text Solution

    |

  12. Evaluate: ("lim")(xtooo)x^(1/x)

    Text Solution

    |

  13. The value of lim(x->pi)(1+cos^3x)/(sin^2x) is (a)1/3 (b) 2/3 ...

    Text Solution

    |

  14. Evaluate: underset(x rarr 0)("lim") ((729)^x-(243)^x-(81)^x+9^x+3^x-1...

    Text Solution

    |

  15. If f(x)=(3x^2+a x+a+1)/(x^2+x-2), then which of the following can be c...

    Text Solution

    |

  16. Evaluate underset(ntooo)lim(-1)^(n-1)sin(pisqrt(n^(2)+0.5n+1)),"where ...

    Text Solution

    |

  17. ("lim")(ntooo)1/(1+nsin^2n x) is equal to (a)-1 (b) 0 (c) 1 (d) ...

    Text Solution

    |

  18. Let the sequence ltb(n)gt of real numbers satisfy the recurrence relat...

    Text Solution

    |

  19. Which of the following true ({.} denotes the fractional part of the ...

    Text Solution

    |

  20. Evaluate: lim(n->oo)(4^n+5^n)^(1/n)

    Text Solution

    |