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UFCalcSet33

UFCalcSet33 - Exercises UF Calculus Set 33 1 The graph of a...

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Unformatted text preview: Exercises UF Calculus Set 33 1. The graph of a function f ( x ) is given below. Let g ( x ) = Z x f ( t ) d t . (a) Write the interval(s) on which g ( x ) is increasing/decreasing. (b) At what points does g ( x ) have local extrema? (c) At what points does g ( x ) attain its absolute extrema on [- 4 , 8 ] ? (d) Write the interval(s) on which g ( x ) is concave up/down. 2. Write the domain of each function g ( x ) . Then calculate g ( x ) . (a) g ( x ) = Z 2 1 3 t 2 + 2 t d t (b) g ( x ) = Z x- 1 √ 4- t 2 t d t (c) g ( x ) = Z 2 √ x t sin( t 2 ) d t (d) g ( x ) = Z x 2 x cos( t ) t d t 3. Evaluate the definite integrals using the Fundamental Theorem of Calculus. (a) Z 1 1 + 4 x 5 d x (b) Z- 4 π- ex d x (c) Z 8 4 8 3 x 5 / 3 d x (d) Z 4 2 2 x + 2 x- 2 d x (e) Z π/ 4 4 sin( x ) + 2 cos(2 x ) d x (f) Z 1 / 3 sec 2 ( πx ) d x (g) Z 16 4 1- √ x x 2 d x (h) Z 16 4 (1- √ x ) 2 2 x d x (i) Z 8 1 x- 1 / 3 (4- x ) d x (j) Z 1- 2 (2- x 2 ) 2 d x (k) Z ln(3) 2 e- x- e 2 x d x (l) Z 1 x 2...
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UFCalcSet33 - Exercises UF Calculus Set 33 1 The graph of a...

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