Life In 19x19

Alright I'll ponder this all over for a while, especially the mistake I made at .

"Probably because some players cut you into pieces and you died many horrible deaths ?"
That made me chuckle by it truthfulness.
B would hane at :b3: — and then ?
$$B :b1: tenuki
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O X . . . . . .
$$ | . . O X ...

It would seem that the best move is to simply follow the joseki rather than deal with the consequences of trying to be fancy.

"Probably because some players cut you into pieces and you died many horrible deaths ?"
That made me chuckle by it truthfulness.
B would hane at :b3: — and then ?
$$B :b1: tenuki
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O X . . . . . .
$$ | . . O X ...

The other homework problem: what happens after :w2: ?
$$B :b1: tenuki
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O X . . . . . .
$$ | . . O X . . . . . ,
$$ | . O X 3 . 5 . . . .
$$ | . O X . . . . . . .
$$ | . . 2 4 . 6 ...

Here's a start: you can use it as a template —
just click the button "quote" and edit as you wish:
$$B :b1: tenuki
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O X . . . . . .
$$ | . . O X . . . . . ,
$$ | . O X 2 3 . . . . .
$$ | . O X 4 8 9 ...

I couldn't create the file correctly. But, In both scenarios I imagine the sequences would go as such:
B D-16 -
W - C-17
B D-17 -
W - C-16
B C-15 -
W - B-15
B C-14 -
W - B-14
Sequence One
B Q-4 -
W - B-13
B C-13 -
W - B-11
End Sequence One
B C-13 -
Sequence Two
W - D-15
B E-15 -
W - D-14
B E-13 ...

I'm pretty sure white's next move would be at C-13 after black tenukis. And I think after white cuts black can either push into white's corner or net the cutting stone.

My best guess would be that the extension instead of the solid connection is to stay ahead of the opponent and keep them sealed in the corner. In the game I made a solid connection because I was afraid of the cut on 15-D. But looking at it now, the cut doesn't seem as severe as I thought and trying ...

I feel this game wasn't over because white was ahead... Can someone explain why my opponent resigned?