In this section we will take a look at the basics of representing a surface with parametric equations
2: Eliminating the Parameter
Example 1
Questions: Find a parametrization of the curve that represents the curve of intersection of eachpair of surfaces
Advanced Physics questions and answers
For the surface represented in parametric form by r(u, v) =< u,u + v, uv >, find the area of this surface for 0 Su Su and
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Question: Problems
Elements of H(2,(4:0:1)) pass through (4:0:1), so 16a11 + 4a13=0, and a generic element of A2({g =
Find a parametrization x of the surface of revolution obtained by revolving about the-axis, the curveα: R→R3given byα (t) = (t,cosht,0), and find the partial velocities of x
Find the area of this surface
There are 3 steps to solve this one
Consider the parametrization of the unit circle given by c (t) = (cos t, sin t) A) Verify that c is parametrized by arc length arc leng
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Question: Find an arc length parametrization of r (t)= etsint,etcost,3et r1 (s)= Find a path that traces the circle in the plane y=−3 with radius r=1 and center (2,−3,−5) with constant speed 2
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Question: ParametrizationFind a parametrization for the showncurve: The axis in front is the y-axisand the z-axis goes upwards
Question: Find an arc length parametrization r1 (s) of the line y = 8x
Find a parametrization of the tangent line to r(t) = (ln(t))i + 1-ºj + 10tk at the point t 1
b) Compute the coefficients of the second fundamental form in the basis {xu,xv}
We reviewed their content and use your feedback to keep the Question: Find an arc length parametrization r1(s) of r(t)= etsin(t),etcos(t),8et Assume t(s)=0 when s=0, and t′(0)>0
Question: Find a vector parametrization of the curve x=−4z2 in the xz-plane
Question: 10
a) y = 3x -4, c (0) = (2,2) c (t)= ( b) y = 3x - 4, C (3) = (2,2) c (t)= (
The portion of the cone z =4/x? +y? between the planes z= 12 and z= 16 Let u=r and v=0 and use cylindrical coordinates to parametrize the surface
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