Evaluate the limit at infinity. f(x) = 4[(x + sin x)/(x)] lim x→∞ f(x) The limit of sinx as x approaches infinity = does not exist, which leaves me with x/x or ∞/∞ = 1 so 4(1)=4? Thanks in advance for the help!
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Originally Posted by Johnny Walker Black Evaluate the limit at infinity. f(x) = 4[(x + sin x)/(x)] lim x→∞ f(x) The limit of sinx as x approaches infinity = does not exist, which leaves me with x/x or ∞/∞ = 1 so 4(1)=4? Thanks in advance for the help! For large x: Therefore your sin(x) term is negligible Edit: Visualise by thinking of a suitably large number - say then . Now what is
Originally Posted by Johnny Walker Black Evaluate the limit at infinity. f(x) = 4[(x + sin x)/(x)] lim x→∞ f(x) The limit of sinx as x approaches infinity = does not exist, which leaves me with x/x or ∞/∞ = 1 so 4(1)=4? Thanks in advance for the help! Now, for all x so as the denominator goes to infinity, goes to 0.
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