In the following exercises, use the Intermediate Value Theorem (IVT). 150. Let h ( x ) = { 3 x 2 − 4 , x ≤ 2 5 + 4 x , x > 2 over the interval [0, 4], there is no value of x such that h(x) = 10, although h(0) < 10 and h(4) > 10. Explain why this does not contradict the IVT.
In the following exercises, use the Intermediate Value Theorem (IVT). 150. Let h ( x ) = { 3 x 2 − 4 , x ≤ 2 5 + 4 x , x > 2 over the interval [0, 4], there is no value of x such that h(x) = 10, although h(0) < 10 and h(4) > 10. Explain why this does not contradict the IVT.
In the following exercises, use the Intermediate Value Theorem (IVT).
150. Let
h
(
x
)
=
{
3
x
2
−
4
,
x
≤
2
5
+
4
x
,
x
>
2
over the interval [0, 4], there is no value of x such that h(x) = 10, although h(0) < 10 and h(4) > 10. Explain why this does not contradict the IVT.
Q2) A: Find the region where ODEs has no limit cycle:
x = y + x³
y=x+y+y³
6
Q3)A: Given H(x,y)=x2-x+ y²as a first integral of an ODEs, find this ODES
corresponding to H(x,y) and show the phase portrait by using Hartman
theorem and by drawing graph of H(x,y)-e. Discuss the stability of
critical points of the corresponding ODEs.
Q/ Write Example
is First integral but not
Conservation system.