Problem (1). Let C be the curve parametrized by c(t) = (tan t, sec t), –

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Parts D and E

Problem (1). Let C be the curve parametrized by c(t) = (tan t, sec t), – <t< }.
(a) Find dy/dr.
(b) Find an equation of the tangent line when t = T/4.
(c) Find lim
t+-1/2+ dx
dy
and lim
dy
+=/2- dx'
(d) Sketch the curve C along with the lines y = mx and y = Mx, where lim
M.
t+/2- dr
(e) Find a Cartesian equation of the parametric curve. Does this match what you see in the sketch from
dy
m and lim
t--1/2+ dr
dy
part (d). Explain.
Transcribed Image Text:Problem (1). Let C be the curve parametrized by c(t) = (tan t, sec t), – <t< }. (a) Find dy/dr. (b) Find an equation of the tangent line when t = T/4. (c) Find lim t+-1/2+ dx dy and lim dy +=/2- dx' (d) Sketch the curve C along with the lines y = mx and y = Mx, where lim M. t+/2- dr (e) Find a Cartesian equation of the parametric curve. Does this match what you see in the sketch from dy m and lim t--1/2+ dr dy part (d). Explain.
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