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“Silent Spring” author Rachel Carson spent significant time studying nature on the North Carolina coast; a lovesick Robert Frost licked his wounds in the Great Dismal Swamp; and a floating theater docked at Bath, N.C., inspired Edna Ferber’s novel “Show Boat,” which became a hit musical. Those are a few of the discoveries author Georgann Eubanks unearths in “Literary Trails of Eastern North Carolina: A Guidebook” (UNC Press, $22), the final installment in the statewide trilogy. More than 250 other novelists, journalists, poets, and playwrights, living and deceased, are examined by Eubanks, who shares their stories and passages of their work while leading readers on 18 driving tours, starting from Raleigh and including farming communities, river country, and coastal towns.