1. The problem statement, all variables and given/known data http://i.minus.com/jbzvT5rTWybpEZ.png [Broken] 2. Relevant equations If a function is differentiable, the function is continuous. The contrapositive is also true. If a function is not continuous, then it is not differentiable. A function is differentiable when the limit definition of its derivative exists. A limit exists when the left and right hand limits are equal. The limit of sinx/x as x approaches 0 is 1. 3. The attempt at a solution Okay I first tried making the function continuous but I found that the function would be continuous for 0. I didn't think this was the right answer because the question asked me to use the limit definition so I applied that. Plus, the converse of the statement if a function is diff. it is continuous isn't necessarily true. The left hand limit is equal to 2. The limit of (2sinx - 0) / (x - 0 ) is 2, using the trig identity mentioned above. The right hand limit only equals 2 when k = 2. The limit of kx / x as x approaches 0 is k, since the x-terms cancel, and the limit is equal to k. K therefore must equal 2 for the left hand and the right hand limits to be equal. Is this the correct solution and approach to this proble?