MA140-01
3/4/09
Midterm Exam
No Calculator Portion
Give it up for ________________________!
Show all your work and explain your answers completely. I cannot give partial credit for answers that are both wrong and
unexplained. Even correct "bottom line" answers that are mysterious and unsupported will not be considered completely correct.
Show me what you are thinking. Try to keep your answers neat and organized so that I can follow them easily.
1.) Find each of the following limits. Do not use LโHรดpitalโs rule.
8 points
(a)
2
2
4 9 2
lim
3 6 4
x
x x
x x
โโ
โ +
โ + +
(b)
2
5 2 1
lim
2
x
x
x
โ
โ โ
โ
2
2 2 2
2
2 2 2
4 9 2
lim
3 6 4
x
x x
x x x
x x
x x x
โโ
โ +
โ+ +
2
5 2 1 5 2 1
lim 2
5 2 1
x
x x
x
x
โ
โ โ โ +
โ
โ
โ +
2
2
9 2
4
lim
6 4
3
x
x x
x x
โโ
โ +
โ + +
2
4 2
lim
( 2)( 5 2 1)
x
x
x x
โ
โ
โ โ +
4
3
โ
2
2 2
lim 1
2
5 2 1
x
x
โ
โ โ
= = โ
โ +
2.)
Use a linear approximation to estimate
3
8.06
.
3 points
3
( ) 8
f x x
= +
2
3
1
'( ) (8 )
3
f x x
โ
= +
0 0 0
( ) ( ) '( )( )
L x f x f x x x
= + โ
( ) (0) '(0)(0.06)
L x f f
= +
1
( ) 2 (0.06)
12
L x
๎ ๎
= +
๎ ๎
๎
๎
( ) 2. 0.005
L x
= +
( ) 2.005
L x
=
