frequent-mistakes-2WBB0.pdf - CALCULUS(2WBB0 FREQUENTLY...

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CALCULUS (2WBB0): FREQUENTLY MADE MISTAKES c MICHIEL HOCHSTENBACH, FALL 2018 Incorrect: x + y = x + y Correct: xy = x y (when x 0, y 0) Incorrect: x ( x - 2) = 1 x = 1 or x - 2 = 1 Correct: x ( x - 2) = 0 x = 0 or x - 2 = 0 Incorrect: The answer is 2 x + 4, so x + 2 (can’t just divide by 2 !) Correct: The answer is 2 x + 4, so 2 ( x + 2) Incorrect: x 2 = 3 x x = 3 (by division by x we lose the solution x = 0) Correct: x 2 = 3 x x = 3 or x = 0 since x ( x - 3) = 0 Incorrect: x 2 = x Correct: x 2 = | x | Incorrect: x 2 = a x = a Correct: x 2 = a x = ± a Incorrect: 2 x +3 = 2 x + 2 3 (not allowed in the denominator, e.g. for x = 1 this is not true) Correct: x +3 2 = x 2 + 3 2 (allowed in the numerator) Incorrect: e x + y = e x + e y Correct: e x + y = e x · e y Incorrect: e - ln( x ) = - x Correct: e - ln( x ) = e ln( x - 1 ) = 1 x Incorrect: Forgetting 1 branch when sketching the graph of xy = 1 (or y = 1 /x ) Correct: This graph has 2 branches Incorrect: f - 1 ( y ) = 1 f ( y ) Correct: x = f - 1 ( y ) is the inverse function of y = f ( x ) (also correct: ( f - 1 ) 0 ( y ) = 1 f 0 ( x ) ) Incorrect: For an arbitrary limit considering lim x a + and lim x a - separately (strictly speaking not incorrect but superfluous)
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