To answer this question, we need to evaluate each option and determine which one is the largest when the value of x lies between 0 and 1.
Option A) x - This option is incorrect because when x lies between 0 and 1, it is smaller than x^2, x^3, and 1/x.
Option B) x^2 - This option is incorrect because when x lies between 0 and 1, x^2 is smaller than x^3 and 1/x.
Option C) 1/x - This option is correct because when x lies between 0 and 1, 1/x is larger than x, x^2, and x^3. As x gets closer to 0, 1/x becomes larger.
Option D) x^3 - This option is incorrect because when x lies between 0 and 1, x^3 is smaller than 1/x.
Therefore, the correct answer is C) 1/x. This option is the largest when the value of x lies between 0 and 1.