Walking on a surface Consider the following surfaces and parameterized curves C in the xy-plane. a. In each case, find z' (t) on C. b. Imagine that you are walking on the surface directly above C consistent with the positive orientation of C. Find the values of t for which you are walking uphill. 56. z = 4 x 2 + y 2 – 2; C : x = cos t , y = sin t , for 0 ≤ t ≤ 2 π
Walking on a surface Consider the following surfaces and parameterized curves C in the xy-plane. a. In each case, find z' (t) on C. b. Imagine that you are walking on the surface directly above C consistent with the positive orientation of C. Find the values of t for which you are walking uphill. 56. z = 4 x 2 + y 2 – 2; C : x = cos t , y = sin t , for 0 ≤ t ≤ 2 π
Solution Summary: The author calculates the value of zprime (t) if the surface and the oriented curve are differentiable functions.
Walking on a surfaceConsider the following surfaces and parameterized curves C in the xy-plane.
a. In each case, find z' (t) on C.
b. Imagine that you are walking on the surface directly above C consistent with the positive orientation of C. Find the values of t for which you are walking uphill.
56. z = 4x2 + y2 – 2; C: x = cos t, y = sin t, for 0 ≤ t ≤ 2π
9.3.16. Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.
(a) about the x-axis (b) about x = 4
please answer both a and b
1 to t to 2
x=4t,
y=sqrt(t^2)
but if you can only do one please do b
You are given a cylinder S in R3 with equation x = z2 + 2.
Let C be the curve in the xz-plane whose equation is the same as that of S. Find the equation of the surface of revolution generated by revolving C about the x-axis.
Find the area of the surface obtained by rotating the curve y = cos 2x, x is an element of [ 0, pi/6 ] about the x-axis.
Chapter 12 Solutions
Calculus: Early Transcendentals, Books a la Carte Plus MyLab Math/MyLab Statistics Student Access Kit (2nd Edition)
University Calculus: Early Transcendentals (4th Edition)
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