Question

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

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