Factual error: The commentary suggests that Sheldon had the correct solution to problem 1 and merely lost points on the quiz because he didn't show his work. In reality he did the first problem incorrectly. Taking the derivative of (x+2) ^2+ (y+1) ^2 = 13 with respect to x yields: 2* (x+2) +2* (y+1) * (dy/dx) = 0 which implies that: dy/dx = - (x+2) / (y+1) and at the point (0,2) this means that the slope dy/dx is actually equal to - (2/3), not 2/3. It is correct that when using the form y=mx+b at the point 0,2 reveals that 2=m*0+b, or that b=2. So the correct equation for the tangent line is y = - (2/3) x + 2, not y = (2/3) x + 2 as shown in the episode. (00:13:55)
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