The second derivative of y x 2 is dy 2 d 2 x 2 Verify that Eq (11) applied to c(t) (t, t 2 ) yields dy 2 d 2 x 2 In fact, any parametrization may be used Check that c(t) (t 3 , t 6 ) and c(t) (tan t, tan 2 t) also yield dy 2 d 2 x 2 ...

For the parametrization ct t 2 we have so that indeed For ct t t we have so that again and xt ...

The second derivative of y = x 2 is dy 2 /d 2 x = 2. Verify

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The second derivative of y = x²is dy²/d²x = 2. Verify that Eq. (11) applied to c(t) = (t, t²) yields dy²/d²x = 2. In fact, any parametrization may be used. Check that c(t) = (t³, t⁶) and c(t) = (tan t, tan²t) also yield dy²/d²x = 2

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Dec 21, 2023 05:57 AM

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The second derivative of y = x 2 is dy 2 /d 2 x = 2. Verify

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For the parametrization ct t 2 we have so that indeed For ct t t we have so that again and xt ...View the full answer

Calculus

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