ENGR 233 Applied Advanced Calculus Quiz 2 Questions And Answers Latest Update 2026/2027

ENGR 233 Applied Advanced Calculus Quiz 2 Questions
And Answers Latest Update 2026/2027

ENGR 233: Applied Advanced Calculus QUIZ #2 – A

1. (50 points) Consider the function f (x, y) = sin−1(y − x − 1).
(a) Sketch the level curves.
(b) Find the directional derivative of the given function at (1,-1) in the direction of negative
x-axis.




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, ENGR 233: Applied Advanced Calculus QUIZ #2 – A 2023-02-09

2. (50 points) Assume that a ball is launched with a speed of 30ft/s from the tip of the building
with a height of 40ft into the air with the angle of θ = 30◦ (consider the ideal situation; assume
the ball doesn’t move/roll when it hits the ground, with no air friction, flat ground, etc.).
(a) Find the maximum altitude and the speed of the ball at this point.
(b) Determine the ball’s height from the ground when it is 40ft far from its launch point,
horizontally.




height




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