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Common mistakes in Calculus C

# Common mistakes in Calculus C - -4 and not 2-x 2-3 x 4 5...

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1 Here is a list of things you can and can not do in mathematics. This list is based on common mistakes made by students. 1. a + b is not equal to a + b . For example, 1 + 1 = 2 = 1 . 41 ... , but 1 + 1 = 1 + 1 = 2 . 2. ( a + b ) 2 is not equal to a 2 + b 2 . For example, (1 + 1) 2 = 2 2 = 4 , but 1 2 + 1 2 = 1 + 1 = 2 . Remember that the formula which is true is ( a + b ) 2 = a 2 + b 2 + 2 ab . 3. Do not break fractions, i.e. a + b c + b is not equal to a c + b d If you want to group the sum a c + b d into a single expression, then you need to use the least common multiple. For example: 3 4 + 2 5 = 5 × 3 + 4 × 2 20 = 23 20 However, something like that is true for muliplication a c b d = ab cd , example: 3 4 × 2 5 = 6 20 4. If you have a minus sign in front of a parenthesis then it changes the sign of every term inside. For example 2 - ( x 2 - 3 x +4) = 2 - x 2 +3 x

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Unformatted text preview: -4 and not 2-x 2-3 x + 4 . 5. You can not simplify summands in fractions, i.e., the following simpli-ﬁcation is wrong : x 2 + 8 x-4 = x 2 + 6 8 x- 6 4 = x 2 + 2 x-1 2 The following are useful rules. 1. a b c d = ad bc (1) i.e., "the ﬁrst times the inverse of the second". For example: 1 2 3 4 = 1 × 4 2 × 3 = 4 6 2. a x a y = a x + y . 3. ( a x ) y = a xy . 4. log( a + b ) is not equal to log( a )+log( b ) . However, the following is true: log( ab ) = log( a )+log( b ) . The statements made here do not depend on which basis of log we are using. 5. log( a b ) = b log( a ) . 6. log( a b ) = log( a )-log( b ) ....
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Common mistakes in Calculus C - -4 and not 2-x 2-3 x 4 5...

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