MAE 3310 COMPREHENSIVE EXAMINATION
TEST 2026 FULL QUESTIONS AND CORRECT
ANSWERS
▶ Use Newton's method with the specified initial approximation x1 to find
x3, the third approximation to the root of the given equation.
x3-3x+1=0, x1=2
(Give your answer to 4 decimal places). Answer: 1.5486
▶ Use the Left-endpoint Rule with n = 4 to approximate the integral.
3 + t^2. Answer: 26
▶ Use the Trapezoidal Rule with n = 6 steps to approximate the integral.
Round your answer to 2 decimal places.
x 2 2.5 3 3.5 4 4.5 5
f(x) 3 2 8 5 7 3 4. Answer: 14.25
▶ Choose f(x) and g(x) such that. Answer: f(x) = x^5, g(x) = \frac{x+1}{x+2}
▶ Simplify [f(x+h)-f(x)] / h for
f(x) = -3x2 +2. Answer: -6x-3h
▶ Find an equation of the tangent line to the curve y=5x3 at the point (-3, -
135).. Answer: y=135x+270
▶ Find an equation of the tangent line to the curve 4x2+3y2=7 at the point
(1, 1).. Answer: y = -1.33x + 2.33
▶ Find a linear approximation for f(x) = x3/2 at x = 1.. Answer: (3x/2) - 1
▶ Find the value or values of c that satisfy the conclusion of the Mean
Value Theorem for the function f(x) = x + 96/x , and interval [6, 16]..
Answer: 4 sqrt6
TEST 2026 FULL QUESTIONS AND CORRECT
ANSWERS
▶ Use Newton's method with the specified initial approximation x1 to find
x3, the third approximation to the root of the given equation.
x3-3x+1=0, x1=2
(Give your answer to 4 decimal places). Answer: 1.5486
▶ Use the Left-endpoint Rule with n = 4 to approximate the integral.
3 + t^2. Answer: 26
▶ Use the Trapezoidal Rule with n = 6 steps to approximate the integral.
Round your answer to 2 decimal places.
x 2 2.5 3 3.5 4 4.5 5
f(x) 3 2 8 5 7 3 4. Answer: 14.25
▶ Choose f(x) and g(x) such that. Answer: f(x) = x^5, g(x) = \frac{x+1}{x+2}
▶ Simplify [f(x+h)-f(x)] / h for
f(x) = -3x2 +2. Answer: -6x-3h
▶ Find an equation of the tangent line to the curve y=5x3 at the point (-3, -
135).. Answer: y=135x+270
▶ Find an equation of the tangent line to the curve 4x2+3y2=7 at the point
(1, 1).. Answer: y = -1.33x + 2.33
▶ Find a linear approximation for f(x) = x3/2 at x = 1.. Answer: (3x/2) - 1
▶ Find the value or values of c that satisfy the conclusion of the Mean
Value Theorem for the function f(x) = x + 96/x , and interval [6, 16]..
Answer: 4 sqrt6
