‫)‪(16) 2.5 Continuity "Intermediate Value Theorem" (I.V.T‬‬
‫‪State the Intermediate Value Theorem‬‬
‫‪Example 1‬‬
‫‪Solution‬‬
‫‪Let‬‬
‫‪(1) continuous function on‬‬
‫)‪(2‬‬
‫‪(3) N any number between‬‬
‫‪and‬‬
‫‪Then‬‬
‫‪such that‬‬
‫حفظ‬
‫طريقة حل مسائل )‪Intermediate Value Theorem (I.V.T‬‬
‫‪1‬‬
‫يكون معطى في المسألة دالة‬
‫و عدد ‪" N‬غلبا ما يكون صفر"‬
‫‪2‬‬
‫نختار عدد و ليكن‬
‫بحيث‬
‫" أو بمعنى آخر‬
‫تكون سالب‬
‫‪3‬‬
‫نختار عدد و ليكن‬
‫بحيث‬
‫" أو بمعنى آخر‬
‫تكون موجبة‬
‫‪4‬‬
‫فيكون‬
‫‪5‬‬
‫نثبت أن الدالة متصلة على الفترة‬
‫أو "‬
‫‪such that‬‬
‫‪6‬‬
‫‪7‬‬
‫"‬
‫إذا كان معطى في المسألة دالتين‬
‫أفرض دالة جديدة‬
‫∴‬
‫وكمل المسألة على الدالة‬
(16)
2.5 Continuity "Intermediate Value Theorem " (I.V.T)
Example 2
54 November
16, 2009 A
P2
Show that the equation
has a real solution
Solution
∴
∴
has a real solution
Example 3
38 March 31,
2004
Use the Intermediate Value Theorem to show that
the equation
has a real root
Solution
∴
∴
Example 4
( 4 points )
60 October 31 Use the intermediate Value Theorem to show that the graphs of the functions
and
intersects
, 2011
Solution
the graph of the functions
and
intersects at
if
Let
∴
graphs of the functions intersect at
HOSSAM GHANEM
86881166
‫حسام غانم‬
(16)
2.5 Continuity "Intermediate Value Theorem " (I.V.T)
Example 5
P3
Use the intermediate Value Theorem to show that there is a root of the
equation
in
Solution
∴
∴
has a real solution
Example 6
68 October 23, 2104
[ 10 pts. ] Use the Intermediate Value Theorem to show the equation
has at least one real solution .
Solution
Let
is cont. on
∴
∴ the equation
such that
has at least one real solution .
Example 7
67 8 March 2014
[ 20 pts. ]
Use the Intermediate Value Theorem to show that If
on
and
,
,
then there is at last one
such that
and
are continuous
Solution
Let
is cont. on
∴
such that
HOSSAM GHANEM
86881166
‫حسام غانم‬
(16)
2.5 Continuity "Intermediate Value Theorem " (I.V.T)
P4
Example 8
47 23 Dec.
2014
Show that the equation
has at least one real root
Solution
Let
∴
the equation
such that
has at least one real root
Homework
1
2
3
4
5
6
7
8
9
44 November 9, 2006
Show that the equation
has a real solution
27 May 30. 2006
Let
Show that the equation
two distinct roots in the interval
.
has at least
55 April 8, 2010
(3pts) Let
of and
and
. Show that the graphs
intersect
57 November 8, 2010
Show that the equation
has a real solution . (3 pts.)
39 5 June, 2011
[ 4 pts. ] Let
be any real number . Show that the equation
has at most one root in
.
59 9 July 2011
[2 pts. ]: Show that the equation
has at least one real solution
46 July 5, 2007
Let
and
Theorem to show that the graphs of f and
.Use the Intermediate Value
intersect at least once
64 March 9, 2013
[ 10 pts. ] Let
and
Theorem to show that the graphs of
.Use the intermediate Value
and g intersect at least once .
Use the I.V.T to show that . The graph of
cuts the x-axis
HOSSAM GHANEM
86881166
‫حسام غانم‬