MTH 252
Fall 2021
Exam 1
代考微积分 Find the angle the resultant force makes with the positive x-axis. You can write your solution for the angle by using the inverse of a trigonometric
Instructions.
- Attempt all questions.
- Show all the steps of your work clearly.
- You are allowed to use a scientifific calculator on this exam. The use of graphing calculators or calculators with symbolic manipulation capabilities is not allowed.
1.Reduce each equation to one of the standard forms, classify the surface, and sketch it: 代考微积分
(a) (8 points) y2 − 6y − x = 7
(b) (8 points) x = y2+ z2 − 2y − 4z + 5
- (a) (10 points) Find the equation of the plane passing through A(1, 2, −2) and contains the line
x = 2t, y = 3 − t, z = 1 + 3t.
(b) (6 points) Find the symmetric equations of a line passing through A and orthogonal to the plane you obtained in part (a).
3.(6 points) Find the values of x such that 代考微积分
are orthogonal.
- (8 points) Find the area of the parallelogram with vertices P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8),and S(5, 2, 7).
5.The resultant force of two forces is the vector obtained as the sum of these forces. 代考微积分
Consider the following forces: Given the forces,
(a) (2 points) Graph the resultant force in the fifigure above.
(b) (9 points) Find the magnitude of the resultant force. Use the approximations 
≈ 1.4 and 
≈ 1.5 if needed to simplify your solution. 代考微积分
(c) (4 points) Find the angle the resultant force makes with the positive x-axis. You can write your solution for the angle by using the inverse of a trigonometric function.
- (15 points) Find the velocity and position vectors of a particle that has the acceleration
7.(12 points) Given the vector function
find 
- (12 points) Find the curvature of the vector function
