2022 Fall Semester Calculus II Midterm Solutions
Problem 1: Solving the System of Linear Equations
(a) Gaussian-Jordan Method:
- Use Gaussian-Jordan elimination to solve the given linear equations.■ Perform forward elimination and back substitution to fin
(b) Inverse Matrix Using Adjugate:
- Find the inverse of coefficient matrix A using the adjugate method.■ Multiply the inverse matrix by the right-hand side vector t
Problem 2: Sequence Convergence
(a) Sequence a_n:■ - Determine convergence by calculating the limit as n approaches infinity.■ - If the sequence is bounded an
Problem 3: Taylor Series Expansion
Find the Taylor series of f(x) = cos(x) centered at x = π/3 up to the 4th term.■The radius of convergence is R = ∞.