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)___

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BANSAL|Exercise All Questions|425 Videos

Similar Questions

Explore conceptually related problems

Consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1, and lim_(x rarr0)((p(x))/(x^(3))-2)=4. Then the value of [P(1)] is (where [.] represents greatest integer function)

Let p(x) be a polynomial of degree 5 having extremum at x=-1,1 and lim_(x rarr0)((P(x))/(x^(3))-1)=7 .The value of |P(2)| is

Let p(x) be a polynomial of degree 4 having extremum at x=1,2 and lim_(x rarr0)(1+(p(x))/(x^(2)))=2. Then find the value of p(2)

Let P(x) be a polynomial of degree 5 having extremum at x= -1 , 1 and underset(x rarr 0)(lim) ((P (x))/(x^(3)) -1)= 7 . The value of |P(7)| is

Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and underset(x to 0) ("lim") (1 + (p(x))/(x^(2)) ) = 2 . Then the value of p(2) is

Let p (x) be a real polynomial of degree 4 having extreme values x=1 and x=2.if lim_(xrarr0) (p(x))/(x^2)=1 , then p(4) is equal to

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

f:(2,3)rarr(0,1) defined by f(x)=x-[x], where [.] represents the greatest integer function.

If x^(2)+x+1-|[x]|=0, then (where [.] is greatest integer function) -

BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. Discuss the extrema of f(x)=x/(1+xtanx),x in (0,pi/2)

    Text Solution

    |

  2. Let f(x)={x^3+x^2+10 x ,\ \ x<0-3sinx ,\ \ \ \ xgeq0 . Investigate x=0...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the maximum perimeter of a triangle on a given base ' a ' and ...

    Text Solution

    |

  5. If lim(x->a) f(x) = lim(x->a) [f(x)] ([.] denotes the greatest intege...

    Text Solution

    |

  6. A function f is defined by f(x)=\ int0^picostcos(x-t)dt ,\ 0lt=xlt=2pi...

    Text Solution

    |

  7. From a fixed point A on the circumference of a circle of radius r , th...

    Text Solution

    |

  8. Show that for each a >0 the finction e^(-a x)dotx^a^2 has a maximum va...

    Text Solution

    |

  9. Let f(x)=x^(3) +3(a-7)x^(2)+3(a^(2) -9) x-1. If f(x) has positive po...

    Text Solution

    |

  10. Show that the surface area of a sphere is the same as that of the l...

    Text Solution

    |

  11. Consider the function represented parametrically as x=a t^2,\ y=2a ...

    Text Solution

    |

  12. Statement-1 : If a1,a2,a3,….. an are positive real numbers , whose pro...

    Text Solution

    |

  13. Find a point on the curve x^2 + 2y^2 = 6, whose distance from the li...

    Text Solution

    |

  14. For the circle x^(2)+y^(2)=r^(2), find the value of r for which the ar...

    Text Solution

    |

  15. If f(x)=x^3+b x^2+c x+d and 0<b^2<c , then f(x) is a strictly increasi...

    Text Solution

    |

  16. Prove that sinx+2xgeq(3x(x+1))/pi, AA x in [0,pi/2] (Justify the ine...

    Text Solution

    |

  17. If P(x) is a polynomial of degree 3 satisfying p(-1)=10 ,p(1)=-6a n dp...

    Text Solution

    |

  18. Let f(x) be a polynomial of degree 3 having a local maximum at x=-1...

    Text Solution

    |

  19. e total number of local maxima and local minima of the function f(x) =...

    Text Solution

    |

  20. Consider the function f:(-oo,\ oo)->(-oo,oo) defined by f(x)=(x^2-a...

    Text Solution

    |