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Refer to the statement of Example 110, a...

Refer to the statement of Example 110, and let `S_(k)` denote the area bounded by `L_(k) and y=x^(2)`, then `3 overset(oo)underset(k=1)Sigma overset(S_(k))/(T_(k)^(2))` is equal to

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Knowledge Check

  • Suppose k in N . In the Cartesian plane, suppose the line L_(k) whose equation is y+x+k(k+1) meets the parabola y=x^(2) at two points A_(k) and B_(k) , Let L_(k) = length of the segment A_(k)B_(k) and T_(k)= area of Delta OA_(k)B_(k) , then overset(n)underset(k=1)Sigma (T_(k))/(L_(k)) is equal to

    A
    `(1)/(6sqrt(2))n(n+1)^(2)`
    B
    `(1)/(6sqrt(2))n^(2)(n+1)`
    C
    `(1)/(6sqrt(2))n(n+1)(2n+1)`
    D
    `(1)/(6sqrt(2))n(n+1)(n+2)`

  • Let m be a positive integer, then S=overset(m)underset(k=1)Sigmak((1)/(k)+(1)/(k+1)+(1)/(k+2)+...+(1)/(m)) is equal to:

    A
    `(1)/(4) m(m+2)`
    B
    `(1)/(4)m(m+3)`
    C
    `(1)/(4)m(m+4)`
    D
    `(1)/(4)m(m+6)`

  • Let A(k) be the area bounded by the curves y=x^(2)+2x-3 and y=kx+1. Then

    A
    the value of k for which A(k) is least is 2
    B
    the value of k for which A(k) is least is `3//2`
    C
    least value of A(k) is `32//3`
    D
    least value of A(k) is `64//3`

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