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(4) Consider the set C = {(x, y) = R² | y² = xº(1-x²)}. (a) Is C a curve? If yes, why yes? If no, why not? (b) Find a parametrisation of C and sketch C. Be sure to specify the domain of your parametrisation. Hint: a nice set of identities to consider are cos² () 2 sin (¹) cos (¹). sin t (c) Find the tangent line to C at (2,4). = 1+cost, sin² (1) 2 - 1-cos t and

(4) Consider the set C = {(x, y) = R² | y² = xº(1-x²)}. (a) Is C a curve? If yes, why yes? If no, why not? (b) Find a parametrisation of C and sketch C. Be sure to specify the domain of your parametrisation. Hint: a nice set of identities to consider are cos² () 2 sin (¹) cos (¹). sin t (c) Find the tangent line to C at (2,4). = 1+cost, sin² (1) 2 - 1-cos t and

Advanced Engineering Mathematics
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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(4) Consider the set C = {(x, y) = R² | y² = xº(1 − x²)}. E (a) Is C a curve? If yes, why yes? If no, why not? (b) Find a parametrisation of C and sketch C. Be sure to specify the domain of your parametrisation. Hint: a nice set of identities to consider are cos² (¹) sin t = 2 sin () COS ; (§). (c) Find the tangent line to C at - 1+cost, sin² () 2 - 1-cost 2 " and
Transcribed Image Text:(4) Consider the set C = {(x, y) = R² | y² = xº(1 − x²)}. E (a) Is C a curve? If yes, why yes? If no, why not? (b) Find a parametrisation of C and sketch C. Be sure to specify the domain of your parametrisation. Hint: a nice set of identities to consider are cos² (¹) sin t = 2 sin () COS ; (§). (c) Find the tangent line to C at - 1+cost, sin² () 2 - 1-cost 2 " and
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