Home
Class 12
MATHS
Consider P(x) to be a polynomial of degr...

Consider `P(x)` to be a polynomial of degree 5 having extremum at `x=-1,1,` and `("lim")_(xvec0)((p(x))/(x^3)-2)=4` . Then the value of `[P(1)]` is (where [.] represents greatest integer function)___

Text Solution

Verified by Experts

The correct Answer is:
2.4
Give `underset(xrarr0)lim p(x)/(x^(3))-2=4`
`therefore underset(xrarr0)lim(p(x))/(x^(3))=6`
consider P(x) =`ax^(5)+bx^(4)+6x^(3)`
Now `P(-1)=0 rarr5a-4b=-018`
and `P(1)=0 rarr 5a+4b=-18`
Hence P(x) =`(-18)/(5)x^(5)+6x^(3)`
or P(1)`=12/3`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|13 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Linked comprehension Type|2 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|48 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Let p(x) be a polynomial of degree 4 having extremum at x = 1,2 and lim_(x->0)(1+(p(x))/x^2)=2. Then find the value of p(2).

lim_(xrarr0) [(100 tan x sin x)/(x^2)] is (where [.] represents greatest integer function).

lim_(xto0) [(1-e^(x))(sinx)/(|x|)] is (where [.] represents the greatest integer function )

If f(x) = (e^([x] + |x|) -3)/([x] + |x|+ 1) , then: (where [.] represents greatest integer function)

Evaluate: ("lim")_(xvec0)(tanx)/x where [dot] represents the greatest integer function

Prove that [lim_(xto0) (tan^(-1)x)/(x)]=0, where [.] represents the greatest integer function.

Evaluate: [("lim")_(xrarr0)(tan^(-1)x)/x], where [.]represent the greatest integer function

Find ("lim")_(xvec0){tan(pi/4+x)}^(1//x)

x→1 lim ​ (1−x+[x−1]+[1−x]) is equal to (where [.] denotes greatest integer function)

If f(x)=[x](sin kx)^(p) is continuous for real x, then (where [.] represents the greatest integer function)

CENGAGE ENGLISH-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Numerical Value Type
  1. L e tf(x)={(|x^3+x^2+3x+sinx|(3+sin(1/x)) ,, x!=0), (0 ,, x=0):} then...

    Text Solution

    |

  2. Leg f(x) be a cubic polynomial which has local maximum at x=-1a n df(x...

    Text Solution

    |

  3. Consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1...

    Text Solution

    |

  4. If m is the minimum value of f(x , y)=x^2-4x+y^2+6y when x and y are s...

    Text Solution

    |

  5. For a cubic function y=f(x),f^(x)=4x at each point (x , y) on it and i...

    Text Solution

    |

  6. Number of integral values of b for which the equation (x^3)/3-x=b has ...

    Text Solution

    |

  7. L e tf(x)={x+2,x<-1x^2,-1lt=x<1(x-2)^2,xgeq1 Then number of times f^(...

    Text Solution

    |

  8. The number of nonzero integral values of a for which the function f(x)...

    Text Solution

    |

  9. L egf(x)={x^(3/5),ifxlt=1-(x-2)^3,ifx >1 Then the number of critical ...

    Text Solution

    |

  10. A right triangle is drawn in a semicircle of radius 1/2 with one of...

    Text Solution

    |

  11. A rectangle with one side lying along the x-axis is to be inscribed in...

    Text Solution

    |

  12. The least integral value of x where f(x)=(log)(1/2)(x^2-2x-3) is monot...

    Text Solution

    |

  13. The least area of a circle circumscribing any right triangle of area 9...

    Text Solution

    |

  14. L e tf(x)={|x^2-3x|+a ,0lt=x<3/2 -2x+3,xgeq3/2 If f(x) has a local m...

    Text Solution

    |

  15. Let f(x)=30-2x -x^3, the number of the positive integral values of x w...

    Text Solution

    |

  16. Let f(x) ={{:(x(x-1)(x-2),(0lexltn),sin(pix),(nlexle2n):} least valu...

    Text Solution

    |

  17. Number of critical point of the function f(X) =x+sqrt(|x|) is .

    Text Solution

    |

  18. consider f(X) =(1)/(1+|x|)+(1)/(1+|x-1|) Let x(1) and x(2) be point wh...

    Text Solution

    |

  19. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  20. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |