calculus

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Find the limit of this calculus problem.?

(5x-3)/(ln(5+4e^(x))

x=inf

  • calculus -

    Intuitive approach
    for large values of x, the 5 of (5 + e^x) becomes insignificant , so for all practical purposes
    we just have to look at ln(4e^x)
    which is ln4 + lne^x
    = ln4 + x
    Also for very large values of x, the constant ln4 is relatively insignificant, so the denominator
    approaches x for large values of x

    Now look at the top.
    Again for large values of x , the -3 becomes meanignless compared to the size of 5x

    So for large values of x
    our expression becomes
    lim 5x/x as x ----> infinity
    = 5

  • calculus -

    5x+2xa-6ab

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