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calculus

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.
lim x→∞ {(5x − 4)/(5x + 3)}^5x + 1

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  1. it is of the form inf/inf.
    taking the derivatives.
    it is not clear to me is the +1 in the exponent or not, I assume not.
    lim= (5)/(5))*(4x)(5)
    lim= 1^inf * 5=5

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  2. lim x→∞ {(5x − 4)/(5x + 3)}^5x
    lim x→∞ {(1 - 7/(5x+3))}^5x
    Let u=5x
    lim u→∞ {(1 - 7/u)}^u

    I assume you can now see that this is e^-7

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