NUMERICAL ANALYSIS 10TH EDITION BY
BURDEN ACTUAL TEST 2026 VERIFIED
QUESTIONS AND ANSWERS COMPREHENSIVE
STUDY GUIDE
◉ List three ways that error associated with Taylor series estimation
of a function can be minimized.
Answer: Solution: a) Reducing the step size b) Increasing the order
of Taylor series (add more terms) . c) Make the equation more linear.
◉ What are the principal two advantages of Newton-Raphson
method compared to Secant method (4 points)?.
Answer: Newton-Raphson method requires only one initial guess
while the secant method requires 2 initial guesses. b) It converges
faster as compared to secant method. c) Is more accurate as
compared to secant method.
◉ Given the following equation: f(x)=5e^x+(2/x)(e^x-1)
Determine if numerical method or analytical method should be used
to solve this problem. Explain your answer. If numerical method
needs to be used, state the name of a method that can be used (6
points)..
Answer: Numerical method should be used to solve this problem as
it is an implicit equation in terms of x. Any root finding method
, (Newton-Raphson Method, Secant Method and Fixed Point Method)
can be used.
◉ List and explain the error type that is only present in numerical
solution of problem. Give one example of a method that can be used
to determine that error (4 points)..
Answer: Error associated with numerical solutions is : Truncation
error: due to approximations in representing exact operations or
quantities. Example is in Taylor series the truncation error is given
by: Rn= fn+1(i)h^(n+1)/((n+1)!)
◉ Explain how optimum step size for a Taylor series estimation of a
function was derived (i.e. what parameters does it depend on in
words. Do not just write symbol) (4 points)..
Answer: Total error is submission of round off and truncation error.
To optimize the total error we will find the minimum of this
submission
◉ Explain what method you would use to solve the following
equation for the unknown, y given x of 3 (3 points). + 10
y=x2 y+ xe-x +10.
Answer: As the equation is implicit in terms of y so any root finding
method (bisection, false position, NewtonRaphson, Secant) can be
used.
BURDEN ACTUAL TEST 2026 VERIFIED
QUESTIONS AND ANSWERS COMPREHENSIVE
STUDY GUIDE
◉ List three ways that error associated with Taylor series estimation
of a function can be minimized.
Answer: Solution: a) Reducing the step size b) Increasing the order
of Taylor series (add more terms) . c) Make the equation more linear.
◉ What are the principal two advantages of Newton-Raphson
method compared to Secant method (4 points)?.
Answer: Newton-Raphson method requires only one initial guess
while the secant method requires 2 initial guesses. b) It converges
faster as compared to secant method. c) Is more accurate as
compared to secant method.
◉ Given the following equation: f(x)=5e^x+(2/x)(e^x-1)
Determine if numerical method or analytical method should be used
to solve this problem. Explain your answer. If numerical method
needs to be used, state the name of a method that can be used (6
points)..
Answer: Numerical method should be used to solve this problem as
it is an implicit equation in terms of x. Any root finding method
, (Newton-Raphson Method, Secant Method and Fixed Point Method)
can be used.
◉ List and explain the error type that is only present in numerical
solution of problem. Give one example of a method that can be used
to determine that error (4 points)..
Answer: Error associated with numerical solutions is : Truncation
error: due to approximations in representing exact operations or
quantities. Example is in Taylor series the truncation error is given
by: Rn= fn+1(i)h^(n+1)/((n+1)!)
◉ Explain how optimum step size for a Taylor series estimation of a
function was derived (i.e. what parameters does it depend on in
words. Do not just write symbol) (4 points)..
Answer: Total error is submission of round off and truncation error.
To optimize the total error we will find the minimum of this
submission
◉ Explain what method you would use to solve the following
equation for the unknown, y given x of 3 (3 points). + 10
y=x2 y+ xe-x +10.
Answer: As the equation is implicit in terms of y so any root finding
method (bisection, false position, NewtonRaphson, Secant) can be
used.
