Description
Find the limit of the function (if it exists). (If an answer does not exist, enter DNE.)
lim x→ln 8
e2x − 64 |
ex − 8 |
Write a simpler function that agrees with the given function at all but one point. Use a graphing utility to confirm your result.
g(x) = |
|
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Explanation & Answer
1. e^(2x) = 8^2
(eˣ)² = 8²
eˣ = 8
logₑ8 = x ← by definition of logarithm
ln(8) = x ← ANSWER
2.
e^(2x) = 8^2
ln(e^(2x)) = ln(8^2)
2x·ln(e) = 2·ln(8)
x = ln(8) ← ANSWER
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