Dual in the simplest form means two
Living "A dual existence" could mean being someone at a particular moment and another person at another moment.
White mentioned being a father in the present and being a son in the remembered life of the past.
This means White was first a "<em>son</em>" to his "<em>father</em>" in the past and he is now a "<em>father</em>" to his "<em>son</em>" in the present. Therefore, he is living two different lives; life as a <em>son</em> and life as a <em>father</em>.
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One of the ways that Lyddie changes is in her attitude towards education. Over the course of the story, she comes to understand the value of formal learning, improving her reading skills by tackling more challenging books and setting herself the goal of attending Oberlin College. Initially, Lyddie arrived at the mill with the sole purpose of providing for her family. But in setting herself the ambitious goal of attending college, whole new vistas of opportunity have opened up to her. To a large extent, Lyddie had been forced to live her life prior to this point through her family, putting their needs ahead of her own. But by the end of the story, Lyddie's come to realize that she's an individual in her own right with her own life to lead. This is another important change that she experiences.
Did you read the passage anyways all you have to do to get your answer is read it’s right there in the passage but your answer is the first one