Analysis Help. Suppose f : (c,∞) → Reals and L ∈ Reals. Formulate a definition for the statement: limx→∞ f(x?
Suppose f : (c,∞) → Reals and L ∈ Reals.
a.) Formulate a definition for the statement: lim as x→∞ f(x) = L.
b.) Use the definition in (a) to prove: lim as x→∞ of (3x-4)/(1-2x) = -(3/2)
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The tricky part here is the x approaching infinity. If we are allowed to assume that if x approaches infinity, then 1/x approaches 0. Then, we can use the traditional definition of limit but replace:
abs(x - a) < delta implies abs(f(x) - L) < epsilon, with:
abs(1/x - a) < delta implies abs(f(1/x) - 1/L) < epsilon
See how that works for you.