‫‪(29) 3.10 Linear Approximations And Differentials‬‬
‫‪The linear approximation‬‬
‫كيف توجد الـ‬
‫‪The Approximate Value‬‬
‫‪Find an approximate value for:‬‬
‫خطوات الحل‬
‫‪1‬‬
‫حدد الـ‬
‫‪2‬‬
‫حدد الـ‬
‫‪3‬‬
‫افرض الدالة‬
‫‪4‬‬
‫اوجد‬
‫‪5‬‬
‫اشتق الدالة لتحصل على‬
‫‪6‬‬
‫أوجد‬
‫‪7‬‬
‫أكتب القانون‬
‫‪8‬‬
‫عوض في القانون‬
‫‪9‬‬
‫اختصر‬
‫وذلك بوضع‬
‫بدال من العدد‬
‫‪Example‬‬
(29) 3.10 linear Approximations and differentials
Example 1
P2
Find the differential of the function
Solution
Example 2
Find the differential of the function
Solution
Example 3
Find the differential of the function
Solution
Example 4
Find the differential of the function
Solution
Example 5
Find the differential of the function
Solution
Example 6
Find the differential of the function
Solution
Example 7
Find the differential of the function
Solution
HOSSAM GHANEM
86881166
‫حسام غانم‬
(29) 3.10 linear Approximations and differentials
Example 8
P3
Find the differential of the function
Solution
Example 9
(a) Find the differential
(b) Evaluate
for
Solution
Example 10
10 June 6 1994
Use differentials to find an approximate value for:
Solution
Let
Example 11
59 December 6 , 2014
Use linear approximation to estimate
.
Solution
Let
HOSSAM GHANEM
86881166
‫حسام غانم‬
(29) 3.10 linear Approximations and differentials
Example 12
P4
Use a linear approximation ( or differentials ) to estimate the given number :
Solution
Let
Example 13
Use a linear approximation ( or differentials ) to estimate the given number :
Solution
Let
Example 14
45 May 10,
2009
Find the linear approximation of
at
Solution
HOSSAM GHANEM
86881166
‫حسام غانم‬
.
(29) 3.10 linear Approximations and differentials
Example 15
52 July 23 , 2011 A
P5
[ 2 + 1 Points ] Let
.
a) Use differentials to find expressions for
and
b) Use the linear approximation formula to estimate
Solution
a)
b)
Example 16
( 3 Points ) Use the linear approximation at
to show that
54 April 29 , 2012
Solution
Let
Example 17
56 November 21 , 2012
Let
a ) Find the differential
b ) Approximate
.
.
Solution
HOSSAM GHANEM
86881166
‫حسام غانم‬
(29) 3.10 linear Approximations and differentials
Example 18
57 April 27 , 2013
P6
Let
.
a ) Find the differential .
b ) Use differentials to approximate
Solution
Let
HOSSAM GHANEM
86881166
‫حسام غانم‬
(29) 3.10 linear Approximations and differentials
P7
Homework
Use differentials to find an approximate value for
1
2 June 12 1990
2
1 December 3, 1992
3
2 May 20, 1993
4
5
6 January 6, 1993
6
11 August 11, 1994 A
7
1 November 1987
8
46 August 1 , 2009
9
44 December 21, 2008
10
36 Dec 15, 2005
11
42 May 5, 2008
12
40 May 3, 2007
13
41 July 19, 2007
14
39 December 14, 2006
15
37 May 4, 2006
16
34 July 22, 2004
17
28 Dec 20, 2001
18
19
26 May 10, 2001
HOSSAM GHANEM
86881166
‫حسام غانم‬
(29) 3.10 linear Approximations and differentials
P8
Homework
43 July 19, 2008
Use differentials to find an approximate value for:
38 July 17, 2006
Use differentials to find an approximate value for:
33 May 6, 2004
1
2
3
Let
4
30 May 15th, 2003
Let
Use differentials to approximate
Use differentials to approximate value
27 August 2, 2001
5
Use linear approximation to estimate
(3 pts.)
where
Let
6
(a) Find
(b) Use linear approximation to estimate
(3 Points) Find the value of
48 Sunday 9 May 2010
.
if
7
49 July 24, 2010
and
changes from
to
8
(3 pts.) Use differentials to approximate
9
[3 pts.] Use linear approximation to estimate
50 22 December 2010
.
10
Use differentials to find an approximate value for:
11
(4 points ) : Use linear approximation to estimate the number
12
13
32 Dec. 18, 2003
Use differentials to find an approximate value for:
Use differentials to approximate :
HOSSAM GHANEM
07/12/2011
8 August 28 , 1993
( 3 Points )
86881166
51 8 May 2011
55 July 14 , 2012
‫حسام غانم‬