Suppose f(x) = sqrt( x + 1).

(a) Carefully sketch a very nice large graph of f(x) without using a graphing utility.

(b) Write down the difference quotient between the points (3; f(3)) and the generic point (x; f(x)). That is, you will want to label the second point as (x; f(x)). On your graph in part (a) include a sketch that clearly shows what quantity the difference quotient represents.

(c) For your difference quotient found in part (b), find the limit as x approaches 3. On your graph in part (a), include a sketch that clearly shows what this limit represents

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