Could someone please help me with:
limit x->infinity (π^x) / (4^x)
Am I supposed to do L'Hopital's?
limit x->infinity (π^x) / (4^x)
Am I supposed to do L'Hopital's?
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limit x->infinity (π^x)/(4^x) =
limit x->infinity (π/4)^x = 0 because π/4 < 1 { definition of exponential function }
limit x->infinity (π/4)^x = 0 because π/4 < 1 { definition of exponential function }
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Let:
y = lim(x-->∞) (π^x) / (4^x)
Then take the natural log of both sides:
ln(y) = lim(x-->∞) ln[(π^x) / (4^x)]
ln(y) = lim(x-->∞) ln((π/4)^x)
ln(y) = lim(x-->∞) xln(π/4)
ln(y) = -∞
y = e^(-∞)
y = 1 / e^(∞)
y = 0
Thus the limit is 0.
y = lim(x-->∞) (π^x) / (4^x)
Then take the natural log of both sides:
ln(y) = lim(x-->∞) ln[(π^x) / (4^x)]
ln(y) = lim(x-->∞) ln((π/4)^x)
ln(y) = lim(x-->∞) xln(π/4)
ln(y) = -∞
y = e^(-∞)
y = 1 / e^(∞)
y = 0
Thus the limit is 0.
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