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[answered] A rectangular shoe-box of width x, length x and height y is


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1.

 

A rectangular shoe-box of width x, length x and height y is of volume 2 so that x2 y = 2.

 

The surface area adds up three rectangular parts of size (x ? y) and 2 square parts of size (x ? x)

 

and leads to

 

f = 2x2 + 3xy .

 

Write down the function f(x) of the single variable x you want to minimize and find the value of

 

x for which the surface area is minimal

 

of theabove

 

( A ) 1 ( B ) 1.145 ( C ) 1.34 ( D ) there is no minimum value ( E ) ? 2.

 

Raindrops increase in size as they fall and so their resistance to falling increases. Suppose a

 

raindrop has an initial downward velocity of 10 m/sec and its downward acceleration is { a ( t )= 9?0.9 t ,if 0? t ? 10

 

0, if t>10

 

If the raindrop is initially 500 m above the ground, how long does it take to fall? of the above

 

( A ) 9.8 s ( B ) 10 s ( C ) 11.8 s ( D ) 13.6 s ( E ) ? 3.

 

The graph of a function f is shown. Which graph is an antiderivative of D f and why? C f A of the above

 

( A ) Graph A ( B ) Graph B ( C ) Graph C ( D ) Graph D ( E ) ? 4.

 

Evaluate the definite integral

 

2 ?(

 

1 2 x+ 1

 

dx

 

x ) of the above

 

37

 

29

 

15

 

5

 

( A ) (B ) (C ) ( D) ( E) ?

 

6

 

6

 

2

 

6 B .

 

5. y' Find

 

x if 2 y=? ? 2 t + 4 dt

 

1 of the above

 

2

 

1

 

1

 

( A ) 2 x ?2 x + 4 ( B ) ?2 x + 4 ( C )

 

( D ) ( ? 2 x 2 + 4? ?6 )? ?6 ( E ) ?

 

3

 

? 2t +4 3

 

2 2 6. f If is integrable on ( a , b)

 

x [ a , b] , then there exists a number x in the open interval such that

 

b ? f =? f

 

a x If your answer is true, then explain your reasoning. If you chose false, then give a

 

counterexample. of the above

 

( A ) True ( B ) False ( C ) not enough information ( D ) ? 7.

 

If f and g are both integrable on [ a , b ] , then f o g If true, explain your reasoning. If false, give a counterexample. of the above

 

( A ) True ( B ) False ( C ) not enough information ( D ) ? is also integrable on [ a , b] .

 


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