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UFCalcSet30

# UFCalcSet30 - Exercises UF Calculus Set 30 1 Find the...

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Exercises UF Calculus Set 30 1. Find the general antiderivative for each function below; assume we have chosen an interval I on which the function is continuous. Several will require an algebraic manipulation ﬁrst. (a) f ( x ) = 4 x 5 (b) f ( x ) = π 10 + ex (c) f ( x ) = 8 9 x 2 / 3 (d) f ( x ) = 2 x + 2 x - 2 (e) f ( x ) = 4 sin( x ) + 2 cos(2 x ) (f) f ( x ) = sec 2 ( πx ) (g) f ( x ) = e - 2 x + e 2 x (h) f ( x ) = (1 + x ) 2 x (i) f ( x ) = x - 1 / 3 (6 - x ) (j) f ( x ) = (1 - 2 x 2 ) 2 (k) f ( x ) = 4 - x 2 - x (l) f ( x ) = x 2 - 1 1 + x 2 2. Find the particular antiderivative F for f ( x ) satisfying the conditions, and write the largest open interval on which F is the antiderivative for f (a) f ( x ) = 2 x + 2 x - 2 ; F passes through ( 1 2 , 4 ) (b) f ( x ) = x - 1 / 3 (6 - x ) ; F ( - 1) = 5 (c) f ( x ) = e - 2 x + e 2 x - sec( x ) tan( x ) ; F (0) = 0 3. Use trigonometric identities to manipulate the functions below in order to ﬁnd the general antiderivative. (a)

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UFCalcSet30 - Exercises UF Calculus Set 30 1 Find the...

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