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I have these two separate strokes - how would I go about connecting them perfectly, so there is no bend where they meet?
You can select both endpoints with the direct select tool (A) and then do Command (or Control)-Option-J to Average the points (the default selection of Both usually works for me). Then Command (or Control)-J to Join the points.
If the anchor points are from different paths you can do this:
1) Select the 2 end-points with the direct select tool (A).
2) At the top bar under the anchor section, select Connect Selected End Points.
Connect Selected End Points
You can then delete one of the anchor points and adjust the curve.
Required, but never shown