(e) Find the point(s) on C where the tangent line is vertical. Do not rely on the graph from (a) – show analytical work to support your findings. Your graph should show that part of the graph of C consists of a loop that begins and ends at (9,0). (f) Use the arc length formula to find the length of that loop. (Be careful when determining bounds for the integral.) (g) Find the area enclosed by the loop. (h) Find the area of the surface obtained by rotating the upper half of the loop about the r-axis. (i) Find a Cartesian equation of the curve C. Hint: square the equation for y and replace the expressions in t in terms of r. Discuss how difficult it would be to answer parts (f)-(h) without the given
(e) Find the point(s) on C where the tangent line is vertical. Do not rely on the graph from (a) – show analytical work to support your findings. Your graph should show that part of the graph of C consists of a loop that begins and ends at (9,0). (f) Use the arc length formula to find the length of that loop. (Be careful when determining bounds for the integral.) (g) Find the area enclosed by the loop. (h) Find the area of the surface obtained by rotating the upper half of the loop about the r-axis. (i) Find a Cartesian equation of the curve C. Hint: square the equation for y and replace the expressions in t in terms of r. Discuss how difficult it would be to answer parts (f)-(h) without the given
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Need help with parts e - i.
Transcribed Image Text:(e) Find the point(s) on C where the tangent line is vertical. Do not rely on the graph from (a) – show
analytical work to support your findings.
Your graph should show that part of the graph of C consists of a loop that begins and ends at (9,0).
(f) Use the arc length formula to find the length of that loop. (Be careful when determining bounds
for the integral.)
(g) Find the area enclosed by the loop.
(h) Find the area of the surface obtained by rotating the upper half of the loop about the r-axis.
(i) Find a Cartesian equation of the curve C. Hint: square the equation for y and replace the expressions
in t in terms of x. Discuss how difficult it would be to answer parts (f)-(h) without the given
parametrization of the curve C.
Transcribed Image Text:11. Let C be the curve with parametrization a =
3t2, y = 3t – t³.
(a) Use a graphing calculator or some computer graphing program (Desmos, wolframalpha.com, etc.)
to sketch the portion of C where -2 <t< 2.
dy
(b) Find
dr
(c) Find the equation(s) of the tangent line(s) to the graph at the point (9,0). (Hint: looking at the
graph from part (a), how many should there be?)
(d) Find the point(s) on C where the tangent line is horizontal. Do not rely on the graph from (a)
show analytical work to support your findings.
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