2301115: Calculus for Business I
Homework III
Due date: 31 August 2022
1
Solving Nonlinear Inequality.
1.x2
✗
10  0
3x
2
[ -75]
C-
2.x + 4 < 0 ∅
3.
x2
1
x
✗ C-
<0
C- 09
x2 + 4x 5
0
x2 + 3x + 2
3x + 2
5.
0 ✗
(x 1)2
✗E C
4.
2
) V
Corll
00 , -27 U
C- or
Ctr 5 ]
-2J ]
Compute the derivative of the following functions using definition only.
1.If p = f (q) =
2.f (x) = 2 + x
p
3.f (x) = x
3
C-
-
-1
1
dp
, find
2q
dq
-1
292
I
=
=
=
Ésx
Di↵erentiate the following functions
:
1.f (x) = 186.5
p
2.f (x) = 30
3.f (x) = 5x
4.F (x) =
1
4x1 0
÷
5.f (x) = x2 + 3x
6.f (x) = 5x8
7.V (r) =
4 2
⇡r
3
4
2×1-3
3x5 + 6
F.
40 ✗
?
-
15 ×
"
"r
1
3
5
8.R(t) = 5t
9.v(t) = t
2
p
1
p
4 3
t
'
'
-
21-1-32, 1Foo
10
x7
10.R(x) =
4
3T¥
-
≥
Find an equation of the tangent line to the
curve at the indicated point.
1.y = 4x2 + 5x + 6; (1, 15)
5
①
1) ✗ 2-3×-1010
( x g2Cxtz≤
•
L
⑤
since
◦
×
'
-
≥
y
f-
>
50
✗ C- [ -45 ]
✗ C-
,
11
ftp..fi?o'-zc9thi'-tzq
1in
a.
hyo
CXty
∅
1in
h-10
Him
0
<
<◦
trio
slim
⊖
-1
⊕
C- 00 ,
-1J
-
O_0
I
since
% :{ 9
"
22
-1in
two
'
↓!? _÷n
2-
,
1-
292
#
CZ.tcx.tn)
-
h
h→o2+×t!
¥49m
zqr
-
2
>
Uc -411
ftp.limfcxthl-fcxsh-oo-h
=/in
it
f'cop :-b
[ -5 , 2)
slim
=
⊕
VCQI )
zqcllttzhh
,
so ,
✗ C-
⊕
1
:
I
#
c
l
"
29 ezqtzh]
-2h
≤°
>
I
{¥4,210
51
•
¥ # ⊕ i. I
o
h-70
h-i.E-a.ae
◦
◦
•
q
-
-
≤°
cxttcxti )
h
i.
2+4×-5
<
[
%
-
✗
41×4-3×+2
< 0
Cxilcxts )
n
I
2442h
¥
X¥
✗ C-
②
13×1-2
≥
solution
No
:
✗ +
3)
✗ 21-430
5 ⊕
⊖
; (4, 3) y
✗ 21-4<0
2)
•
i
.
x2
1
2.y =
-
-7510×-8
"
×
¥
CAH
•
o
o
-0%+0 ! -01+0
✗ c- Coo,
-3 ]
>
3)
fixation
h-iofathh-kx-il.tn
SETH
h-10
✗ th
h-10
1in
1-
WE
fcxjz
:
h-20
f- 4×228×1-5
=D
1¥43
y
≥
-
1×4-2×4144
1in 4cxthP+scxth> +61-444-5×+6)
slim
15-4=13
✗ 7- xhtxhth '
h→o
h→o
slope it'll
(Xthlcxth ]
4×2+5×+6
=/in
i.
×
Acth tix )
h→o
fix)
Cufflinks
A-
h→o
1)
-
Eth
ihcxth Trx )
Him
④
A
h
:(in
=
-
DX
13×1-2 #
h
4*+8×4+412
# tghtb-4*2-15×-61
h
8th +5h
=
µ
8kt
Note :
where
gone ?