Precalculus
Precalculus
11th Edition
ISBN: 9780135189405
Author: Michael Sullivan
Publisher: PEARSON
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Chapter 14.2, Problem 28AYU
To determine

To find: lim x → 1 ( 2x + 1 ) 5/3

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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.

Chapter 14 Solutions

Precalculus

Ch. 14.1 - Prob. 11AYUCh. 14.1 - Prob. 12AYUCh. 14.1 - Prob. 13AYUCh. 14.1 - Prob. 14AYUCh. 14.1 - Prob. 15AYUCh. 14.1 - Prob. 16AYUCh. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - Prob. 20AYUCh. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - Prob. 22AYUCh. 14.1 - Prob. 23AYUCh. 14.1 - Prob. 24AYUCh. 14.1 - Prob. 25AYUCh. 14.1 - Prob. 26AYUCh. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - Prob. 28AYUCh. 14.1 - Prob. 29AYUCh. 14.1 - Prob. 30AYUCh. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - Prob. 32AYUCh. 14.1 - Prob. 33AYUCh. 14.1 - Prob. 34AYUCh. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - Prob. 38AYUCh. 14.1 - Prob. 39AYUCh. 14.1 - Prob. 40AYUCh. 14.1 - Prob. 41AYUCh. 14.1 - Prob. 42AYUCh. 14.1 - In Problems 43-48, use a graphing utility to find...Ch. 14.1 - Prob. 44AYUCh. 14.1 - Prob. 45AYUCh. 14.1 - Prob. 46AYUCh. 14.1 - Prob. 47AYUCh. 14.1 - In Problems 43-48, use a graphing utility to find...Ch. 14.2 - Prob. 1AYUCh. 14.2 - Prob. 2AYUCh. 14.2 - Prob. 3AYUCh. 14.2 - Prob. 4AYUCh. 14.2 - Prob. 5AYUCh. 14.2 - Prob. 6AYUCh. 14.2 - Prob. 7AYUCh. 14.2 - Prob. 8AYUCh. 14.2 - In Problems 7- 42, find each limit algebraically....Ch. 14.2 - Prob. 10AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 12AYUCh. 14.2 - Prob. 13AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 17AYUCh. 14.2 - Prob. 18AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 21AYUCh. 14.2 - Prob. 22AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 24AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 26AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 28AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 30AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 34AYUCh. 14.2 - Prob. 35AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 39AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 41AYUCh. 14.2 - Prob. 42AYUCh. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - Prob. 44AYUCh. 14.2 - Prob. 45AYUCh. 14.2 - Prob. 46AYUCh. 14.2 - Prob. 47AYUCh. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - Prob. 49AYUCh. 14.2 - Prob. 50AYUCh. 14.2 - Prob. 51AYUCh. 14.2 - Prob. 52AYUCh. 14.2 - In problems 53-56, use the properties of limits...Ch. 14.2 - Prob. 54AYUCh. 14.2 - Prob. 55AYUCh. 14.2 - In problems 53-56, use the properties of limits...Ch. 14.3 - For the function f( x )={ x 2 ifx0 x+1if0x2...Ch. 14.3 - Prob. 2AYUCh. 14.3 - Prob. 3AYUCh. 14.3 - Prob. 4AYUCh. 14.3 - Prob. 5AYUCh. 14.3 - Prob. 6AYUCh. 14.3 - Prob. 7AYUCh. 14.3 - Prob. 8AYUCh. 14.3 - Prob. 9AYUCh. 14.3 - Prob. 10AYUCh. 14.3 - Prob. 11AYUCh. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - Prob. 14AYUCh. 14.3 - Prob. 15AYUCh. 14.3 - Prob. 16AYUCh. 14.3 - Prob. 17AYUCh. 14.3 - Prob. 18AYUCh. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - Prob. 20AYUCh. 14.3 - Find lim x 4 f( x ) .Ch. 14.3 - Prob. 22AYUCh. 14.3 - Find lim x 2 f( x ) .Ch. 14.3 - Prob. 24AYUCh. 14.3 - Does lim x4 f( x ) exist? If it does, what is it?Ch. 14.3 - Prob. 26AYUCh. 14.3 - Is f continuous at 4 ?Ch. 14.3 - Prob. 28AYUCh. 14.3 - Is f continuous at 0?Ch. 14.3 - Prob. 30AYUCh. 14.3 - Is f continuous at 4?Ch. 14.3 - Prob. 32AYUCh. 14.3 - Prob. 33AYUCh. 14.3 - Prob. 34AYUCh. 14.3 - Prob. 35AYUCh. 14.3 - Prob. 36AYUCh. 14.3 - Prob. 37AYUCh. 14.3 - Prob. 38AYUCh. 14.3 - lim x 2 + x 2 4 x2Ch. 14.3 - lim x 1 x 3 x x1Ch. 14.3 - lim x 1 x 2 1 x 3 +1Ch. 14.3 - Prob. 42AYUCh. 14.3 - Prob. 43AYUCh. 14.3 - Prob. 44AYUCh. 14.3 - Prob. 45AYUCh. 14.3 - Prob. 46AYUCh. 14.3 - Prob. 47AYUCh. 14.3 - Prob. 48AYUCh. 14.3 - f( x )= x+3 x3 c=3Ch. 14.3 - Prob. 50AYUCh. 14.3 - Prob. 51AYUCh. 14.3 - Prob. 52AYUCh. 14.3 - Prob. 53AYUCh. 14.3 - Prob. 54AYUCh. 14.3 - Prob. 55AYUCh. 14.3 - Prob. 56AYUCh. 14.3 - f( x )={ x 3 1 x 2 1 ifx1 2ifx=1 3 x+1 ifx1 c=1Ch. 14.3 - Prob. 58AYUCh. 14.3 - Prob. 59AYUCh. 14.3 - Prob. 60AYUCh. 14.3 - Prob. 61AYUCh. 14.3 - Prob. 62AYUCh. 14.3 - Prob. 63AYUCh. 14.3 - Prob. 64AYUCh. 14.3 - Prob. 65AYUCh. 14.3 - Prob. 66AYUCh. 14.3 - Prob. 67AYUCh. 14.3 - Prob. 68AYUCh. 14.3 - f( x )= 2x+5 x 2 4Ch. 14.3 - Prob. 70AYUCh. 14.3 - Prob. 71AYUCh. 14.3 - Prob. 72AYUCh. 14.3 - Prob. 73AYUCh. 14.3 - Prob. 74AYUCh. 14.3 - Prob. 75AYUCh. 14.3 - Prob. 76AYUCh. 14.3 - Prob. 77AYUCh. 14.3 - Prob. 78AYUCh. 14.3 - Prob. 79AYUCh. 14.3 - Prob. 80AYUCh. 14.3 - Prob. 81AYUCh. 14.3 - Prob. 82AYUCh. 14.3 - Prob. 83AYUCh. 14.3 - Prob. 84AYUCh. 14.3 - Prob. 85AYUCh. 14.3 - Prob. 86AYUCh. 14.3 - Prob. 87AYUCh. 14.3 - Prob. 88AYUCh. 14.3 - Prob. 89AYUCh. 14.3 - Prob. 90AYUCh. 14.4 - Prob. 1AYUCh. 14.4 - Prob. 2AYUCh. 14.4 - Prob. 3AYUCh. 14.4 - lim xc f( x )f( c ) xc exists, it is called the...Ch. 14.4 - Prob. 5AYUCh. 14.4 - Prob. 6AYUCh. 14.4 - Prob. 7AYUCh. 14.4 - Prob. 8AYUCh. 14.4 - Prob. 9AYUCh. 14.4 - f( x )=2x+1 at ( 1,3 )Ch. 14.4 - Prob. 11AYUCh. 14.4 - Prob. 12AYUCh. 14.4 - Prob. 13AYUCh. 14.4 - Prob. 14AYUCh. 14.4 - Prob. 15AYUCh. 14.4 - Prob. 16AYUCh. 14.4 - Prob. 17AYUCh. 14.4 - Prob. 18AYUCh. 14.4 - Prob. 19AYUCh. 14.4 - Prob. 20AYUCh. 14.4 - Prob. 21AYUCh. 14.4 - Prob. 22AYUCh. 14.4 - Prob. 23AYUCh. 14.4 - Prob. 24AYUCh. 14.4 - Prob. 25AYUCh. 14.4 - Prob. 26AYUCh. 14.4 - Prob. 27AYUCh. 14.4 - Prob. 28AYUCh. 14.4 - Prob. 29AYUCh. 14.4 - Prob. 30AYUCh. 14.4 - Prob. 31AYUCh. 14.4 - Prob. 32AYUCh. 14.4 - Prob. 33AYUCh. 14.4 - Prob. 34AYUCh. 14.4 - Prob. 35AYUCh. 14.4 - Prob. 36AYUCh. 14.4 - Prob. 37AYUCh. 14.4 - Prob. 38AYUCh. 14.4 - Prob. 39AYUCh. 14.4 - Prob. 40AYUCh. 14.4 - Prob. 41AYUCh. 14.4 - Prob. 42AYUCh. 14.4 - Prob. 43AYUCh. 14.4 - Prob. 44AYUCh. 14.4 - Prob. 45AYUCh. 14.4 - Prob. 46AYUCh. 14.4 - Prob. 47AYUCh. 14.4 - Prob. 48AYUCh. 14.4 - Instantaneous Velocity on the Moon Neil Armstrong...Ch. 14.4 - Prob. 50AYUCh. 14.5 - In Problems 29-32, find the first five terms in...Ch. 14.5 - Prob. 2AYUCh. 14.5 - Prob. 3AYUCh. 14.5 - Prob. 4AYUCh. 14.5 - In Problems 5 and 6, refer to the illustration....Ch. 14.5 - Prob. 6AYUCh. 14.5 - Prob. 7AYUCh. 14.5 - Prob. 8AYUCh. 14.5 - Prob. 9AYUCh. 14.5 - Prob. 10AYUCh. 14.5 - Prob. 11AYUCh. 14.5 - Prob. 12AYUCh. 14.5 - Prob. 13AYUCh. 14.5 - Prob. 14AYUCh. 14.5 - Prob. 15AYUCh. 14.5 - Prob. 16AYUCh. 14.5 - Prob. 17AYUCh. 14.5 - Prob. 18AYUCh. 14.5 - Prob. 19AYUCh. 14.5 - Prob. 20AYUCh. 14.5 - Prob. 21AYUCh. 14.5 - Prob. 22AYUCh. 14.5 - Prob. 23AYUCh. 14.5 - Prob. 24AYUCh. 14.5 - In Problems 23-30, an integral is given. (a) What...Ch. 14.5 - Prob. 26AYUCh. 14.5 - Prob. 27AYUCh. 14.5 - Prob. 28AYUCh. 14.5 - Prob. 29AYUCh. 14.5 - Prob. 30AYUCh. 14.5 - Prob. 31AYUCh. 14.5 - Prob. 32AYUCh. 14 - In Problems, find the limit. Ch. 14 - In Problems, find the limit. Ch. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - Prob. 5RECh. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - In Problems 1215, determine whether fis continuous...Ch. 14 - Prob. 15RECh. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RECh. 14 - In Problems, use the accompanying graph of ....Ch. 14 - In Problems 1627, use the accompanying graph of...Ch. 14 - In Problems, use the accompanying graph of . Find...Ch. 14 - In Problems, use the accompanying graph of . Does...Ch. 14 - In Problems 1627, use the accompanying graph of...Ch. 14 - In Problems, use the accompanying graph of . Is...Ch. 14 - Discuss whether is continuous at and . Use limits...Ch. 14 - Determine where the rational function is...Ch. 14 - In Problems, find the slope of the tangent line to...Ch. 14 - In Problems 3032, find the slope of the tangent...Ch. 14 - In Problems, find the slope of the tangent line to...Ch. 14 - In Problems 3335, find the derivative of each...Ch. 14 - In Problems 3335, find the derivative of each...Ch. 14 - In Problems 3335, find the derivative of each...Ch. 14 - In Problems 36 and 37, approximate the derivative...Ch. 14 - In Problems and, approximate the derivative of...Ch. 14 - Instantaneous Velocity of a Ball In physics it is...Ch. 14 - Instantaneous Rate of Change The following data...Ch. 14 - Prob. 40RECh. 14 - Prob. 41RECh. 14 - Prob. 42RECh. 14 - Prob. 43RECh. 14 - Prob. 44RECh. 14 - Prob. 1CTCh. 14 - Prob. 2CTCh. 14 - Prob. 3CTCh. 14 - Prob. 4CTCh. 14 - Prob. 5CTCh. 14 - Prob. 6CTCh. 14 - Prob. 7CTCh. 14 - Prob. 8CTCh. 14 - Prob. 9CTCh. 14 - Prob. 10CTCh. 14 - Prob. 11CTCh. 14 - Prob. 12CTCh. 14 - Prob. 13CTCh. 14 - Prob. 14CTCh. 14 - Prob. 15CTCh. 14 - Prob. 16CTCh. 14 - An object is moving along a straight line...
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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY