Question

Problem #2: Consider the differential equation with parameter $a > 0$: $x' = \sin(x) - ax$ (a) Find an interval for $a$ where the zero equilibrium point is a sink. Do not include the bifurcation point. The answer is of the form $(c, d)$. Enter the values of $c$ and $d$ (in that order) into the answer box below, separated with a comma. (b) What is the name of the bifurcation of the zero equilibrium point? (c) Explore the behavior of the function $y = \frac{\sin x}{x}$ and find the number of equilibrium points for $a = 0.116$. Problem #2(a): Enter your answer symbolically, as in these examples (A) saddle-node bifurcation (B) supercritical pitchfork bifurcation (C) imperfect bifurcation (D) transcritical bifurcation (E) sub-critical pitchfork bifurcation Problem #2(b): Select Problem #2(c):

          Problem #2: Consider the differential equation with parameter $a > 0$:
$x' = \sin(x) - ax$
(a) Find an interval for $a$ where the zero equilibrium point is a sink. Do not include the bifurcation point. The
answer is of the form $(c, d)$. Enter the values of $c$ and $d$ (in that order) into the answer box below, separated
with a comma.
(b) What is the name of the bifurcation of the zero equilibrium point?
(c) Explore the behavior of the function $y = \frac{\sin x}{x}$ and find the number of equilibrium points for $a = 0.116$.
Problem #2(a):
Enter your answer symbolically,
as in these examples
(A) saddle-node bifurcation (B) supercritical pitchfork bifurcation (C) imperfect bifurcation
(D) transcritical bifurcation (E) sub-critical pitchfork bifurcation
Problem #2(b): Select
Problem #2(c):

Problem #2: Consider the differential equation with parameter a > 0:
x' = sin(x) - ax
(a) Find an interval for a where the zero equilibrium point is a sink. Do not include the bifurcation point. The
answer is of the form (c, d). Enter the values of c and d (in that order) into the answer box below, separated
with a comma.
(b) What is the name of the bifurcation of the zero equilibrium point?
(c) Explore the behavior of the function y = (sin x)/(x) and find the number of equilibrium points for a = 0.116.
Problem #2(a):
Enter your answer symbolically,
as in these examples
(A) saddle-node bifurcation (B) supercritical pitchfork bifurcation (C) imperfect bifurcation
(D) transcritical bifurcation (E) sub-critical pitchfork bifurcation
Problem #2(b): Select
Problem #2(c):

Added by Diana F.

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