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(11.4) In polar coordinates, x = r cos 0 and y = r sin 0. The definition of x implies that = cos 0 (11.40) dr r But we also have x² + y² = r², so differentiating with respect to r gives 2x dr 2r dr (11.41) But eqns 11.40 and 11.41 imply that dr (11.42) dr What's gone wrong?

(11.4) In polar coordinates, x = r cos 0 and y = r sin 0. The definition of x implies that = cos 0 (11.40) dr r But we also have x² + y² = r², so differentiating with respect to r gives 2x dr 2r dr (11.41) But eqns 11.40 and 11.41 imply that dr (11.42) dr What's gone wrong?

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11-4) Please write very well written and legible. Write the answer regularly. I give a positive score to the regular answer.

(11.4) In polar coordinates, x = r cos 0 and y = r sin 0. The definition of x implies that = cos 0 (11.40) dr But we also have x? + y? = r², so differentiating with respect to r gives 2x 2r (11.41) dr But eqns 11.40 and 11.41 imply that dr (11.42) dr What's gone wrong?
Transcribed Image Text:(11.4) In polar coordinates, x = r cos 0 and y = r sin 0. The definition of x implies that = cos 0 (11.40) dr But we also have x? + y? = r², so differentiating with respect to r gives 2x 2r (11.41) dr But eqns 11.40 and 11.41 imply that dr (11.42) dr What's gone wrong?
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