Show That in spherical coordinates a curve given by the parametric equation ρ = ρ t , θ = θ t , ϕ = ϕ t for a ≤ t ≤ b has arc length L = ∫ a b d ρ d t 2 + ρ 2 sin 2 ϕ d θ d t 2 + ρ 2 d ϕ d t 2 d t
Show That in spherical coordinates a curve given by the parametric equation ρ = ρ t , θ = θ t , ϕ = ϕ t for a ≤ t ≤ b has arc length L = ∫ a b d ρ d t 2 + ρ 2 sin 2 ϕ d θ d t 2 + ρ 2 d ϕ d t 2 d t
1. For the parametric equations:
x = 4t3, y=2 + 60t – 8t2, find:
a) All values of t at which the
tangent line has slope 1.
d?y
b)
dx2
Describe and sketch the parametric curve in R³ given by
x = cos t,
y = sin t,
z = sin 2t
For the parametric curve described by the equations x = t and y = Int ,
a) sketch the curve.
b) eliminate the parameter and find the Cartesian equation for the curve.
c) verify that the curve is always concave down for t>0.
(1)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY