Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13, Problem 37SP
To determine
To find:The given line integral.
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x (u, v) = (u² -
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Chapter 13 Solutions
Calculus
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- 4. The particle moves along a plane curve y = e, where x and y are measured in meters. It has a constant speed v= 12 m/s. Determine the x and y components of acceleration at y = 1 m. Also determine the tangential and normal components of acceleration at this instant.arrow_forwardQuestion B1 a. Calculate the line integral (F-dr, where F = 3x y'i + 2x'yj for the curve C. Here C is the curve y = 2x with x ranging from -1 to +1. b. If the vector F is a force, a line integral like (F•dr can be interpreted as the work that this force does on a small object, as it moves along this curve. If the object had an energy of 20 Joules at the start of the path, how much energy would the object have at the end of the path?arrow_forward8. Given the vector r(t) = (sin t, cost, In(cos t). find the equation of the tangent line in parametric form to this curve i =- 4. whenarrow_forward
- 2. For this entire page, let r(t) = (4 sin(t), 3t, 4 cos(t)) (a) Circle the correct graph for the curve traced by r(t) for 0 ≤ t ≤ 4T. Z Y O. W Z Y Х (b) Calculate the vector r(0). Draw this vector in an appropriate location on your chosen graph above. x Y X (c) Calculate the vector r'(0). Draw this vector in an appropriate location on your chosen graph above. (d) Calculate the arc length of this curve from 0 ≤t≤ 47. Show all your work and give an exact answer.arrow_forward5. Consider the force field F = (xy)i + (x −y)j and C, the straight line from the point (-1,2) to (3,3). (a) Find a parameterization of the straight line C. Show your process for this. Include the range of values of the parameter in your final answer. I (b) Express the work done by the field F along the line C as a line integral. Then convert that line integral into a single-variable integral.arrow_forwardPlease help. This problem involves finding the amount of work done over a path using a line integral. Thank you.arrow_forward
- c. r(t) = cos (t - /2)i + sin (t d. r(t) = (cos t)i – (sin 1)J• 20 %3D %3D niz mil e. r(t) = cos (r)i + sin (12)j, t0 v 38. Motion along a circle Show that the vector-valued function %3! r(1) = (2i + 2j + k) + cos t il + sin i + j+ k V3 describes the motion of a particle moving in the circle of radius 1 centered at the point (2, 2, 1) and lying in the plane x + y - 2z = 2. 39. Motion along a parabola A particle moves along the top of the s bai 1 smit %3Darrow_forward14. Consider the two vector-valued functions given by 1 r(t) = (t+1, cos 1+t and w(s) = (s, sin (), ). a. Determine the point of intersection of the curves generated by r(t) and w(s). To do so, you will have to find values of a and b that result in r(a) and w(b) being the same vector. b. Use the value of a you determined in (a) to find a vector form of the tangent line to r(t) at the point where t = a.arrow_forward
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