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Calculus homework

Calculus homework

Calculus homework MATH
T E S T – 4 B U N K E R H I L L C O M M U N I T Y C O L L E G E M A T – 231

N a m e___________________________________

P L E A S E S H O W A L L Y O U R W O R K A N D W R I T E Y O U R W O R K A S N E A T L Y A S P O SSI B L E :

1) F i n d the der i vat i ves o f the f o l l o w i n g f u nct i o ns :

a) y = l n 2 3×9

b ) y = 3

e3x

2) L et f (x) = l n (x) x

a) F i n d the der i vat i ve, f ‘ (x) . b) So l ve f’ (x) = 0

F i n d the i n de f i n i te i ntegra l.

3) x2 x3 + 3 d x

4) F i n d the i n de f i n i te i n teg ra l : x2

x – 1 d x

5) Use su bst i tu t i o n to f i n d the i n de f i n i te i n tegra l : d x

2x l n x

6) F i n d th e i n de f i n i te i n tegra l b y su bst i tu t i o n:

l n (5x) x

d x

7) E va l uate us i n g su bst i tu t i o n : 2

1

( x – 1 ) 2 – x d x

8) E va l uate, g i ve the exact va l ue :

1

0

e x

1 + e x d x

9) F i n d t he area o f the sh aded reg i o n:

10) T he de ma n d f u nct i o n f or a certa i n p r o d uct is g i ven b y p = – 0.01 x2 – 0.2 x + 12 w here p rep resen ts the u n i t p r ice i n d o l lars an d x is t he q uan t i ty dem an ded measu red i n u n i ts o f a th ousan d. D eter m i ne the co nsu mer su r p l us i f the p r ice i s set at $ 4 .

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