The strain S on a solid object depends on the external tension force F (in Newtons) acting on the solid and on the cross-sectional area A (in m2) according to the model S = 5 × 10 − 6 · F A Find the strain for a rod with a cross-sectional area of 8.75 × 10 − 3 m 2 and a tension force of 2.45 × 10 5 N .
The strain S on a solid object depends on the external tension force F (in Newtons) acting on the solid and on the cross-sectional area A (in m2) according to the model S = 5 × 10 − 6 · F A Find the strain for a rod with a cross-sectional area of 8.75 × 10 − 3 m 2 and a tension force of 2.45 × 10 5 N .
Solution Summary: The author explains the strain for a rod with cross sectional area of 8.75times 10-3m
The strain
S
on a solid object depends on the external tension force
F
(in Newtons) acting on the solid and on the cross-sectional area
A
(in m2) according to the model
S
=
5
×
10
−
6
·
F
A
Find the strain for a rod with a cross-sectional area of
8.75
×
10
−
3
m
2
and a tension force of
2.45
×
10
5
N
.
The OU process studied in the previous problem is a common model for interest rates.
Another common model is the CIR model, which solves the SDE:
dX₁ = (a = X₁) dt + σ √X+dWt,
-
under the condition Xoxo. We cannot solve this SDE explicitly.
=
(a) Use the Brownian trajectory simulated in part (a) of Problem 1, and the Euler
scheme to simulate a trajectory of the CIR process. On a graph, represent both the
trajectory of the OU process and the trajectory of the CIR process for the same
Brownian path.
(b) Repeat the simulation of the CIR process above M times (M large), for a large
value of T, and use the result to estimate the long-term expectation and variance
of the CIR process. How do they compare to the ones of the OU process?
Numerical application: T = 10, N = 500, a = 0.04, x0 = 0.05, σ = 0.01, M = 1000.
1
(c) If you use larger values than above for the parameters, such as the ones in Problem
1, you may encounter errors when implementing the Euler scheme for CIR. Explain
why.
#8 (a) Find the equation of the tangent line to y = √x+3 at x=6
(b) Find the differential dy at y = √x +3 and evaluate it for x=6 and dx = 0.3
Q.2 Q.4 Determine ffx dA where R is upper half of the circle shown below.
x²+y2=1
(1,0)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY