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For any positive integer lim( x -> a) (x...

For any positive integer `lim_( x -> a) (x^n-a^n)/(x-a) = na^(n-1)`

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The correct Answer is:
`"False"`
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For any positive integer lim_(x rarr a)(x^(h)-a^(n))/(x-a)=na^(n-1)

lim_ (x rarr a) (x ^ (n) -a ^ (n)) / (xa) = n * a ^ (n-1)

Knowledge Check

  • lim_(x to a) (x^(n) -a^(n))/(x-a) =

    A
    `na^(n)`
    B
    `na^(n-1)`
    C
    0
    D
    does not exist

  • For all positive integers n gt 1 , {x (x^(n-1) - na^(n-1)) + a^(n) ( n-1) } is divisible by

    A
    (x-a)
    B
    x-a
    C
    2(x-a)
    D
    x+a

  • For any positive integer n, int (dx)/(x^(n+1)+x) is equal to

    A
    `1/n log_e( x^n/(x^n+1))+C`
    B
    `1/n log_e( x^n/(x^n+1))+C`
    C
    `1/n log_e( x^n/(x^n+1))+C`
    D
    `1/(n+1) log_e( x^n/(x^n+1))+C`

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