IN: We are to rest in the fact that we are declared righteous because of Christ's sacrifice for us.
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OUT: we are to rest in the fact that we are declared righteous because of christ's sacrifice for us.

IN: So don't miss this unsual concert!
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OUT: so don't miss this unsual concert!

IN: As it moves north it switches from having a westward movement relative to the Earth's surface to having an eastward movement.
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OUT: as it moves north it switches from having a westward movement relative to the earth's surface to having an eastward movement.

IN: In 1830, at the age of 45, Dupin married Rosalie Anne Joubert.
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OUT:
in 1830, at the age of 45, dupin married rosalie anne joubert.