'Name:............,.r.......:........
1. (20pts)
(a) Find the derivative of the function / (r) = .'/5s + 4 W 'rsingthe limit definition for derivative.
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t
- K
P
't----'a
Vf*+(( * Ufrf{
l
/\
[st+ c) -LTv*4 )
-- l,^
( + -Y')
\-
t+L
=
(UFfi+ffiff1
= !,^
e->K
r(ti
!dT(\tWr{#l
G
zE*+4 /
/1
(b) Find the formulafor the line tangentto f(Q ar r = |
r n' ' L ' U ) -5-, - ,
r\stq
{ c r ) = G ?=t<
L
- K1) = r r , [ x , - r )
L.,r
0
rrt-\
d
"
Ir-t)
2. (10 pts) Approximatethe valueof VIfOt Uy using,l-inearApproximalion.
fur= etr;
2r^^\
fLSrl=
or -
z a-=32porrnf
rulie-
4'(x) = |- t x'"t-u,
-\/9
'
tr'-^\
tlSU
--3Vzl
|
=t.O
( s L ' o l- a ) # r a )
+
H
{
t
a
)
f : z---i.ot
- L
t
+ (o,ot)
80
2 .o oot L Y
\:rrre:...........................
3. (.10pts)Fircl the ibllorving dcrivativeslState the deriv:rtive rules tLrtt ]'ou usedl
(n) .i (") = cot (r3 + c") + 5r
(b) y-
( s i n( c o sr ) ) ( l n ( r ' ) )
f,,
j
r 10).
slll'z
( d ) ) ( t ): e ' " ' " - s h r ( l + 5 )
l . ( 1 0 p t s )F i n c lt h e l o r n l l r l ao f t h e l i n e l a D l t c n t o l n ( r : y+ 1 ) + y ! + s i n 1 2 g ; + , 1 . r ' : 1 a t ,( 1 . 0 )
Name:
5. (20pts) A baseball diamond is a square with sides 90 feet long. Suppose a bareball player is
advaneing from second to third base at the rate 24 feet per second, and an umpire is standing on
home plate. Let d be the angle betweenthe third baselineand the line of sight from the umpire to
the runner.
(a) How fast is d changing when ihe runner is 30 feet from the third base?
fl-r{r1h4
---!-
O
4fttr;
F
E, ''t
i
Ax-
-"ti
cr.T
=-r'+
A*lg' J g
7lt r - - 3 o
s(
,q o-V'ixr,
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-
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, -
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. suJ&, /
trs.#
e r
arr q0
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s
= - - l
l!
t
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2-O
w
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to\1
0
J
s.i0 =B
c4
JD = -0,L{ "A""f**^S
--i7
oLt
(b) IIow fast is the distance betweeu the umpire and the runner changing when the runner is 30
feet from the third base?
$\r..L,^.,
---
x L t t o t -- ,E, 1
r
l,J of V "
2 x " o-'1',,*l
ttt
d ; V , n .h l
"-
dfl \y. =bo
i
-- 2 _ \)r ^ . UvL-
oruL
d6
= 1(t""j;) -17
2.Go)d-zQ)
dv
i
Js = 4t4ti-:
ll
(lLY
p
L.
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