Answered step by step
Verified Expert Solution
Question
1 Approved Answer
Assume the function f is defined as f(x)=2.7cosx8.5sinxf(x)=2.7cosx8.5sinx Use the corresponding derivative rules to find the second derivative f(x)f(x) and evaluate that second derivative at
- Assume the function f is defined as f(x)=2.7cosx8.5sinxf(x)=2.7cosx8.5sinx
- Use the corresponding derivative rules to find the second derivative f(x)f(x) and evaluate that second derivative at x = 5.1. Be sure your calculator is in radians mode. Note: To avoid round-off error, retain at least eight decimal places in your calculations.
- Use the "central difference formula for the second derivative" to estimate f(x)f(x) at x = 5.1 for four different values of the mesh sizes
- h = 0.2
- h = 0.1
- h = 0.05
- h = 0.025
- Use your calculated values to fill in this table:
h | central difference approximation | exact second derivative | error = approximation - exact value |
---|---|---|---|
0.2 | |||
0.1 | |||
0.05 | |||
0.025 |
Note: To avoid round-off error, retain the maximum possible number of decimal places in calculations of the error.
- Answer the following two questions:
- Does the error in the central difference approximation drop as the mesh size h is reduced?
- As the mesh size h is reduced by a factor of 2, by what factor is the error in the central difference approximation reduced?
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started