# 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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