Peaks and valleys The following functions have exactly one isolated peak or one isolated depression ( one local maximum or minimum ) . Use a graphing utility to approximate the coordinates of the peak or depression. 63. h ( x , y ) = 1 − e − ( x 2 + y 2 − 2 x )
Peaks and valleys The following functions have exactly one isolated peak or one isolated depression ( one local maximum or minimum ) . Use a graphing utility to approximate the coordinates of the peak or depression. 63. h ( x , y ) = 1 − e − ( x 2 + y 2 − 2 x )
Solution Summary: The author illustrates how to sketch the graph of the function h(x,y)=1-e- (x2+y
Peaks and valleysThe following functions have exactly one isolated peak or one isolated depression (one local maximum or minimum). Use a graphing utility to approximate the coordinates of the peak or depression.
63.
h
(
x
,
y
)
=
1
−
e
−
(
x
2
+
y
2
−
2
x
)
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
Q1/ Two plate load tests were conducted in a C-0 soil as given belo
Determine the required size of a footing to carry a load of 1250 kN for the
same settlement of 30 mm.
Size of plates (m) Load (KN) Settlement (mm)
0.3 x 0.3
40
30
0.6 x 0.6
100
30
Qx 0.6z
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
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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