anonymous
  • anonymous
Could someone explain the part (on http://web.mit.edu/wwmath/calculus/differentiation/chain-proof.html ) after it says "Differentiablility implies continuity; therefore..." Why does du→0 as dx→0
Mathematics
katieb
  • katieb
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amistre64
  • amistre64
hard to follow the proof on that but: think of 2 gears that mesh together at the edges; as one rotates the other rotates. We can call the main gear U, and the gear that U spins is then Y The energy to spin this setup is X. As the change in X goes to zero, the speed of gear U goes to 0; and since gear Y depends on U; as U goes to 0 so does Y. This is the "chain" rule. Y depends on U: y(u(x)) U depends on X: u(x) the change in Y depends in X; dy/dx thru U: dy/dx = dy/du du/dx
amistre64
  • amistre64
if Y is not contiuous with U, then there is a point where Y is not depending on U for its change in momentum right?

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