All 3 Uses

earnest
in
Into the Wild
(Edited)

After a few minutes spent exchanging earnest banalities, we went our separate ways.
p. 73.5

earnest = sincere

editor's notes: The expression earnest banalities is occasionally seen in literature. It refers to something said sincerely but which is too commonplace to be noteworthy.
On weekends, when his high school pals were attending "keggers" and trying to sneak into Georgetown bars, McCandless would wander the seedier quarters of Washington, chatting with prostitutes and homeless people, buying them meals, earnestly suggesting ways they might improve their lives.
p. 113.7 *

earnestly = sincerely
I believe that every man who has ever been earnest to preserve his higher or poetic faculties in the best condition has been particularly inclined to abstain from animal food, and from much food of any kind…
p. 167.8

earnest = sincere and determined

Definitions:

(1) (earnest)
characterized by sincere belief

or:

intensely or excessively serious or determined
(2) (meaning too rare to warrant focus)
Earnest can also be used as a name (variant spelling of Ernest), or to signify the seriousness of a pledge made (as when earnest money is included with an offer to purchase a home).