MAE 3310 ACTUAL EXAM SCRIPT 2026
QUESTIONS WITH SOLUTIONS GRADED A+
▶ If a ball is thrown into the air with a velocity of 58 ft/s, its height (in feet)
after t seconds is given by H=58t-11t2. Find the velocity when t = 4..
Answer: 30ft/s
▶ Find an equation of the tangent line to the curve y = 1/x^2 + 1 at the
point (-2, 1/5). Answer: y = 0.16x + 0.52
▶ Find the tangent line to the ellipse x2/16+y2/4=1 at the point (2,-sqrt3)..
Answer: y = 0.288x-2.308
▶ The radius r of a sphere is increasing at the rate of 0.1 (cm/s). At what
rate (in cm3/s) is the volume V of the sphere increasing when r =
7cm?Round your answer to 2 decimal places.. Answer: 61.58
▶ Find the value or values of c that satisfy the conclusion of the Mean
Value Theorem for the function f(x) = ln (x - 2), and interval [3, 6].Round to
the nearest thousandth.. Answer: 4.164
▶ Find the minimum of the product of two numbers with the property that
the first minus 5 times the second is 7.. Answer: -2.45
▶ 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.
QUESTIONS WITH SOLUTIONS GRADED A+
▶ If a ball is thrown into the air with a velocity of 58 ft/s, its height (in feet)
after t seconds is given by H=58t-11t2. Find the velocity when t = 4..
Answer: 30ft/s
▶ Find an equation of the tangent line to the curve y = 1/x^2 + 1 at the
point (-2, 1/5). Answer: y = 0.16x + 0.52
▶ Find the tangent line to the ellipse x2/16+y2/4=1 at the point (2,-sqrt3)..
Answer: y = 0.288x-2.308
▶ The radius r of a sphere is increasing at the rate of 0.1 (cm/s). At what
rate (in cm3/s) is the volume V of the sphere increasing when r =
7cm?Round your answer to 2 decimal places.. Answer: 61.58
▶ Find the value or values of c that satisfy the conclusion of the Mean
Value Theorem for the function f(x) = ln (x - 2), and interval [3, 6].Round to
the nearest thousandth.. Answer: 4.164
▶ Find the minimum of the product of two numbers with the property that
the first minus 5 times the second is 7.. Answer: -2.45
▶ 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.
