Lim x - > infinity ((e^ (3x)) - (e^ (-3x))) / ((e^ (3x)) + (e^ (-3x)))

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Mathematics

Jayvon Shields

27 April, 19:09

Lim x - > infinity ((e^ (3x)) - (e^ (-3x))) / ((e^ (3x)) + (e^ (-3x)))

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Fitzpatrick · Answer 1

When x approaches to + ∞ the function e^ 3x becomes much bigger then e^ - 3x, which obviously means that e^ - 3x can be neglected in both numerator and denominator.

Here's how I figured this out:

lim x →+∞ = (e^ (3x)) - (e^ (-3x)) / (e^ 3x)) + (e^ (-3x)) = lim x → + ∞ e^ 3x / e^ 3x = 1