Section 14.4: Tangent Planes

The tension \(T\) in the string of the yo-yo in the figure is
\[ T = \frac{mgR}{2r^2 + R^2} \]
where \(m\) is the mass of the yo-yo and \(g\) is acceleration due to gravity. Use differentials to estimate the change in the tension if \(R\) is increased from 3 cm to 3.1 cm and \(r\) is increased from 0.7 cm to 0.8 cm. Does the tension increase or decrease?