In a sizzling debut last week on the New York Stock Exchange, investors sent stock in LinkedIn, the social-networking site for business professionals, soaring 109 percent on its first day of trading. While the enthusiasm subsided a tad the next day, LinkedIn’s shares still closed the week at around $93, more than twice the company’s initial offering price. This put the value of the company, which made $15 million in profit last year, at more than $8 billion.