MAT 101 GRADED EXAM 4 TOPIC 14 2026 STUDY GUIDE COMPLETE QUESTIONS AND ANSWERS 100% CORRECT

MAT 101 GRADED EXAM 4 TOPIC 14 2026
STUDY GUIDE COMPLETE QUESTIONS AND
ANSWERS 100% CORRECT

◉ T/F
Cramer's Rule can be used to solve a system of equations. Answer:
True


◉ T/F
The Gauss Quadrature formulas we discussed in class are called
Gauss-Legendre formulas Answer: True


◉ T/F
Naive Gauss Elimination fails if the pivot element is zero. Answer:
True


◉ T/F
Two applications where numerical integration is used are:
1. integrating discrete data points
2. when it is difficult or impossible to obtain an analytic solution.
Answer: True

, ◉ A single application of Simpson's 1/3 Rule requires computing the
value of the function at how many points? Answer: 3


◉ T/F
The trapezoid rule can be derived from the method of undetermined
coefficients. Answer: True


◉ T/F
Romberg's method is a Newton-Cotes method. Answer: True


◉ T/F
Adaptive Quadrature uses more segments in regions where the
function changes slowly. Answer: False


◉ Evaluate the integral
int(1,7) [(25/x)(sin(x))]dx
using a composite application of the trapezoidal rule with n=2.
Answer: clear, clc
f = @(x) (25/x)*sin(x); % function
a = 1; b = 7; % bounds
n = 2;
h = (b - a)/n;
I_trap_comp = h/2*(f(a) + 2*f(a + h) + f(b))