Concept explainers
The surface with parametric equations
where
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Essential Calculus: Early Transcendentals
- Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?arrow_forwardWrite parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.arrow_forwardfind parametric equations for the line tangent tothe curve of intersection of the surfaces at the given point. urfaces: x2 + y2 = 4, x2 + y2 - z = 0 Point: (√2, √2, 4)arrow_forward
- find parametric equations for the tangent line to the curve of the intersection of the following two surfaces: F(x,y,z) = x^2+y^2+2y+z^2 =3 G(x,y,z) = x^2+y^2-2y+z^2= 3 at the point P=(0,0,square root 3)arrow_forwardFind the area of the surface generated by revolving the curve x = 2 cos θ, y = 2 sin θ, 0 ≤ θ ≤ π/2 about (a) the x-axis and (b) the y-axis.arrow_forwardFind parametric equations for the tangent line at (1, 3, 3) to the curve of intersection of the surface z = x²y and (a) the plane x = 1 (b) the plane y = 3.arrow_forward
- Consider the equation of the surface S given by: exyz + x3z3 − 3y4 = 9 An equation for the plane tangent to S, at the point (1, 0, 2), is given by:arrow_forwardFind the areas of the surfaces generated by revolving the curves about the indicated axesx = ln (sec t + tan t) - sin t, y = cos t, 0≤ t ≤ p/3; x-axisarrow_forwardConsider the parametric equations x = a cos3 t and y = a sin3 t with 0 ≤ t ≤ π. Find the surface area of the solid obtained by rotating the region about the x-axis.arrow_forward
- Find the area of the surface generated by revolving the parametric curve x = cos² t, y = sin² t (0 ≤ t ≤ π/2) about the y-axis.arrow_forwardfind parametric equations for the line tangent tothe curve of intersection of the surfaces at the given point. Surfaces: x2 + 2y + 2z = 4, y = 1 Point: (1, 1, 1 > 2)arrow_forwardDetermine the surface area obtained when the curve with parametric equations x = 4t, y=t^3, 0 < t <1 is rotated about the x-axis.arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage