The following is a (wrong) proof by induction that each nonnegative integer equals twice itself, i. e. n=2n for all integers n≥0. Base case n=0 : P(n) holds for n=0. Inductive step: let us assume that n=2n holds for some nonnegative integer n. We multiply both sides of this equation by the quantity n+1n. This yields n+1=2(n+1), which is P(n+1) . This completes the proof

The edge of a cube was found to be 30 cm with a possible error in measurement of 0.4 cm. use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (round your answers to four decimal places.) (a) the volume of the cube maximum possible error cm3 relative error percentage error % (b) the surface area of the cube maximum possible error cm2 relative error percentage error %