The volume of wood in a tree varies jointly as the height and the square of the girth. Girth is the distance around. If the volume is 35 cubic feet, when the height is 20 feet and the girth is 5 feet, what is the height when the volume is 85.75 cubic feet and the girth is 7 feet?
Converting to a base and floating points
The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. (See attached file for full problem description)
The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. (See attached file for full problem description) Use three digit rounding arithmetic...
The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. (See attached file for full problem description) Determine the number of significant decimal digits and the number of significant binary...
Floating point number systems....
The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. (See attached file for full problem description) IBM System/390 mainframes provide three floating point number systems....
Finite Differences : Difference Quotients, Formulas and Rate of Convergence
1. (Finite Differences) Let f(x) = cos(x+2). Compute f’(0) using the difference quotients given below and step-size h = 2^-n, n = 1,... .5. D + f = (f(x + h) - f(x))/h D o f= (f(x+h)_f(xh))/2h For each difference formula, make a table with the following information. column 1: h column 2: Df column 3: f’(0) — Df column ...continues
Taylor Polynomials : Degrees and Plotting
2. (Taylor polynomials) (a) Write down the Taylor polynomials Pn(x) of degree n = 0, 1, 2,3 for the function f(x) = ln x about the point x = 1. (h) Plot the polynomials Pn(x) and the function f(x) on the interval [0, 3] using Matlab. Describe how the error |f(x) — Pn(x)| behaves with respect to the point x and the degree n. ...continues
Rootfinding and Optimization : Newton's, Secant, Bisection, False Position Methods
3. (Rootfinding and Optimization) (a) Suppose that f is differentiable on [a, b]. Discuss how you might use a rootfinding method to identify a local extremum of f inside [a, b]. (b) Let f(x) = logx — cosx. Prove that f has a unique maximum in the interval [3,4]. (NB: log means natural logarithm.) (c) Approximate this local ma ...continues
Fixed Point : Fixed-Point Iteration and Error Estimate
Please see the attached file for the fully formatted problem.
Limits and Rate of Convergence (4 problems)
Find Limits and Rate of Convergence. Please see the attached file for the fully formatted problems.
