"); grf.document.close(); } function expcls(){ grf.window.close(); } function tip(){ popup=window.open('','','toolbar=no,width=350,height=100,location=top'); popup.document.open(); popup.document.writeln("the intermediate value theorem for continuous functions "); popup.document.writeln("For any continuous function f (x) in the interval [a,b] which satisfies f (a) * f (b) < 0 must have a zero of  'f ' in the interval [a,b] ."); popup.document.writeln(""); popup.document.close(); } function tipclose(){ popup.window.close(); } function hlts(){ hlt=window.open('','','toolbar=no,width=350,height=250,location=top'); hlt.document.open(); hlt.document.writeln("highlights"); hlt.document.writeln("AdvantagesDisadvantages."); hlt.document.writeln(""); hlt.document.close(); } function hltsclose(){ hlt.window.close(); }  
 

3. Find the root of  x - exp(-x) = 0

exp3.jpg for x-exp[-x]

   The graph of this equation is given in the figure. 

   Let a = 0 and b = 1 
 

Iteration
No.
a
b
c
f(a) * f(c)
1
0
1
0.5
0.107 (+ve)
2
0.5
1
0.75
-0.03 (-ve)
3
0.5
0.75
0.625
-9.56*10-3 (-ve)
4
0.5
0.625
0.562
7.758 *10-4(+ve)
5
0.562
0.625
0.593
-3.317*10-4 (-ve)
6
0.562
0.593
0.577
-1.307*10-4 (-ve)
7
0.562
0.577
0.569
-2.978*10-5 (-ve)
8
0.562
0.569
0.565
2.078*10-5 (+ve)

   So one of the roots of   x - exp(-x) = 0 is approximately 0.565.