Suppose that . Then . Thus, there is an iterate such that . By fact 1 given above (in question) this implies that the orbit diverges to infinity.
Now suppose that , so that . Since , we have
Equivalently, . Notice that this implies because and . Thus, the above calculation holds for , and we get
By induction, we get for all integers . Since , and , we have and
Therefore,
which shows that the orbit diverges to infinity.
(1) Consider the polynomial map C → C defined by z-Plz) 22 + c, c E...
E O = 22. 0 22. 41 Z 4 C OO 4 smo letol vagi 7. When FeS reacts with oxygen, Iron 711) oxide and sulfur dioxide form. If 0.600kg of fés reacts with oxygen gas at 25°C and 725 torr, how many liters of sulfur dioxide will be collected? gas3 isht pressures offurrent gases Wesent in the wool ! 7. When solid potassium chlorate decomposes, potassium chloride (s) and oxygen gas astoa form. How many liters of oxygen are...
Here you are asked to prove the Fundamental Theorem of Algebra a different way by using Rouché's Theorem. Where n E N, consider the polynomial n-1 Pn (z)z" k-0 Using the circular contour C-[z : zR with R appropriately chosen, (a) prove that pn(2) has (counting multiplicity) precisely n zeros in the open disc D(0, R); (b) also show that Pn(z) has no zeros in C \ D(0, R) Here you are asked to prove the Fundamental Theorem of Algebra...
using discrete structures 3. Consider the function F(x, y, z) for x, y, z z 0 defined as follows: a. F(x, y, 0)-y+1 b. F(x, 0, 1)-x c, F(x, 0, 2) = 0 d. F(x, 0, z+ 3)-1 e. F(x, y, z)-F(x, F(x, y-1, z), z-1) Using Induction, prove the following a. F(x, y, 1)-x +y b, F(x, y, 2) = xy c. F(x, y, 3)-xy 3. Consider the function F(x, y, z) for x, y, z z 0 defined...
6. Consider the sphere S cut out by z2 + y2 22. Maximize (Daf)P where y, z) 2y +3z and u is a unit vector in the tangent plane to S at the point (A) v3 (E) 2v3 (B) 1+2V2 (C) 2 v3 (G) 3/2 (D) V2 6. Consider the sphere S cut out by z2 + y2 22. Maximize (Daf)P where y, z) 2y +3z and u is a unit vector in the tangent plane to S at the...
(2) Consider the function f : R → R defined by Í 1 x E [-L,0) f(x + 2L) = f(z) -(x) f( 2L) o E l0,L) a. Graph f on the interval [-3L, 3L]. b. Compute Fi-L,Lf) c. Graph F-L(f) on the interval [-3L,3L] c. Graph Fi-L/2,L/() on the interval [-3L,3L]. (2) Consider the function f : R → R defined by Í 1 x E [-L,0) f(x + 2L) = f(z) -(x) f( 2L) o E l0,L) a....