7. Consider the curve x 3t4 + 4t3 + 100, y = 3t - t°, -2

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 22E
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please do a and b

7. Consider the curve x = 3t + 4t3 + 100, y = 3t - t°, -2 <t< 2.
dy
What is
dx
dy
when t = 1?
dx
(a) Find
(b) Find the points on the curve where the tangent is horizontal or vertical.
d²y
(c) Find
dx2
(d) Find an integral expression for the surface area of the surface obtained by rotating the curve
around the y-axis. DO NOT EVALUATE the integral.
Transcribed Image Text:7. Consider the curve x = 3t + 4t3 + 100, y = 3t - t°, -2 <t< 2. dy What is dx dy when t = 1? dx (a) Find (b) Find the points on the curve where the tangent is horizontal or vertical. d²y (c) Find dx2 (d) Find an integral expression for the surface area of the surface obtained by rotating the curve around the y-axis. DO NOT EVALUATE the integral.
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