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10.20 - Questions about the midterm exam Reminder Your...

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Questions about the midterm exam? Reminder: Your cheat sheet must be WRITTEN or TYPED by you. The exam will cover up through (and including) section 2.5 (the chain rule). True-false questions on pages 138–139: 1. “If f is continuous at a , then f is differentiable at a .” ..?. . False! (See the note on page 88.) The converse is however true. 2. “If f and g are differentiable, then ( d / dx ) [ f ( x )+ g ( x )] = f ( x ) + g ( x ).” ..?. . True! 3. “If f and g are differentiable, then ( d / dx ) [ f ( x ) g ( x )] = f ( x ) g ( x ).” ..?. . False! (See the warning before the Product Rule on page 106.) E.g. take f ( x ) = g ( x ) = x .

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4. “If f and g are differentiable, then ( d / dx ) [ f ( g ( x ))] = f ( g ( x )) g ( x ).” ..?. . True! But someone might think that ( d / dx ) [ f ( g ( x ))] = f ( g ( x )), e.g., ( d / dx ) sin x 2 = cos 2 x . Or they might think that ( d / dx ) [ f ( g ( x ))] = f ( x ) g ( x ), e.g., ( d / dx ) sin x 2 = (cos x ) 2 x . 5. “If
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10.20 - Questions about the midterm exam Reminder Your...

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