Questions and Answers #4 Parametric Equations - Edubirdie

University:
Rice University
Course:
MATH 102 | Single Variable Calculus II
Academic year:

2022
Views:

28

Pages:

8
Author:

MathMonk

Questions and Answers Sheet 4 Parametric Equations Question #1 Convert the Cartesian coordinates (-5,-12) into polar coordinates where r >0 and 0𝑜 ≤ 𝜃 ≤ 360𝑜 . Hence, write the other two polar coordinates that represent the point. Answer: Question #2 Write an equation in the indicated coordinate system. Also write a parametric equation and a vector equation for the following equation 𝑥 2 + 𝑦 2 = 25 𝑖𝑛 𝑅3 , cylindrical coordinates, sherical coordinates Answer: Question #3 Write an equation in the indicated coordinate system. Also write a parametric equation and a vector equation for the following equation 𝑥 2 + 𝑦 2 = 100 𝑖𝑛 𝑅2 , polar coordinates Answer: Question #4 Find parametric equations for x, y, and z in terms of the polar coordinates r and 𝜃 to determine the points on the portion of the paraboloid x + y + z = 5 that is on or above the plane z=4 Answer: Question #5 Convert the point from rectangular coordinates to spherical coordinates. (−3, −3, √2) Answer: Question #6 Consider the parametric equations: 𝑥 = 𝑒𝑡 𝑦 = 3𝑒 −2𝑡 Find dy/dx at the point (1.3) Answer: Question #7 Express the point with polar coordinates 𝑝(2, −𝜋/4) in rectangular coordinates Answer: Question #8 Determine the line integral along the curve C from A to B. Find the parametric form of the curve C. Use the vector field: 𝐹⃗ = [−𝑏𝑥𝑐𝑦] Use the following values: a=5;b=2;c=3 Answer: Question #9 Find 𝑑3 𝑦 𝑑𝑥 3 2 for the following parametric equation: 𝑥 =𝑡 −3 𝑦 = 𝑡8 t=2 Answer: Question #10 Find all points (if any) of horizontal and vertical tangency to the curve: 𝑥 = 1 − 𝑡; 𝑦 = 𝑡 2 Answer:

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