Find the real root of x2 = 0.7 using 3 iterations of the bisection method with a = 0.5, b = 2.
Find ALL real roots of f (x) = −2+6x−4x2 +0.5x3 using Newton’s Method with ǫ = 0.01.
The sum of 2 numbers is 20. If we add to each number its square root, the product of both sums is 155.55. Find the two numbers with ǫ = 10−4
The following equation is used to compute monthly payments on a mort-gage:
= Pi 1 − (1 + i)−N
Where A is the total mortgage amount, P is the monthly payment, i is the monthly interest rate, and n is the number of months.
Suppose that a client wants an $800,000.00 mortgage to be paid in 30 years but he can pay no more than $7,000.00 each month. What is the highest monthly interest rate that he would be able to pay?
Enumerate all the elements in fL(2, 2, −1, 1)
Use the bisection method to find a root of x3 − 7x2 + 14x − 6 = 0 in [1, 3.2] with ǫ = 10−2
If P (x) = 10x3 − 8.3x2 + 2.295x − 0.21141 = 0
Find a root using the bisection method with a = 0.25, b = 0.3 and ǫ = 10−3
Now use Newton’s Method to find a root using x0 = 0.28. Explain.
Find an accurate value of
f (x) =
r
1 + x
− 1
1
for large values of x. Compute
lim x f (x)
X→∞
1
