1.2.7 Proving the Limit of An Exponential Function (Epsilon - Delta Definition of A Limit)

[_bit]

saved me on my midterm but i could feel his dread emanating from my speakers

[kingbeauregard]

At 1:34, are we doing a valid step? It's true that, in an equation, you can hit both sides with the same operator and the equation still holds; but it does not necessarily work the same with inequalities. Like if I say x < y, it doesn't necessarily hold that sin(x) < sin(y). If x = pi/2 and y = 3*pi/2, then x < y, but sin(x) > sin(y). That's a situation where it clearly breaks down. How do we make sure it doesn't break down in the current situation? Is it sufficient that the ln() operator doesn't introduce extrema?