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If f(x)=(x+1)(x+2)(x+3)dot(x+n) then f'(...

If `f(x)=(x+1)(x+2)(x+3)dot(x+n)` then `f'(0)` is `n !` (b) `(n(n+1))/2` `(n !)(ln\ n !)` (d) `n !(1+1/2+1/3+1/4+\ dot+1/n)`

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Knowledge Check

  • If f (x+1)+ f (x-1)=2 f (x) and (0)=0, then f (1),n in N is

    A
    nf(1)
    B
    `[ f (1)]^n`
    C
    ` 0`
    D
    None

  • If f(x)=(1+x)^(n) , then the value of f(0)+f'(0)+(1)/(2!)f''(0)+…+(1)/(n!)f^(n)(0) is

    A
    n
    B
    2n
    C
    `2^(n-1)`
    D
    none of these

  • If f(x) = x^n then the value of f(1) +(f '(1) )/(1!) +(f'' (1))/(2!) +(f' ' ' (1))/( 3!) + . . . + (f ^n (1))/( n!) is

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

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