The Mitchell branch of the New Haven Free Public Library tries to be at the forefront of whatever products are trendy or new. That means offering e-books for patrons of all ages and providing computers for children who want to conduct research online or play games. But, according to branch manager Sharon Lovett-Graff, the library’s youngest patrons, and their parents, remain interested primarily in borrowing print books. “At one time, we were all very nervous that e-books would take over. But not anymore,” said Lovett-Graff, who estimates that in the past year, the library checked out about 5,300 board books — thick, picture books aimed at pre-readers.