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1. Vector Functions and Space Curves a) Find the domain of the vector function: r(t) = (√4 — t², e−³t, ln(t + 1)) e-3t t² b) Find the limit: lime¯³ti+ -j + cos 2t k sin² t t-0 c) Sketch the curve with the given vector equation. Indicate with an arrow the direction in which increases: r(t) = (sint, t)

1. Vector Functions and Space Curves a) Find the domain of the vector function: r(t) = (√4 — t², e−³t, ln(t + 1)) e-3t t² b) Find the limit: lime¯³ti+ -j + cos 2t k sin² t t-0 c) Sketch the curve with the given vector equation. Indicate with an arrow the direction in which increases: r(t) = (sint, t)

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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show full & complete procedure HANDWRITTEN only. Please answer parts a), b) & c). Note they are subparts of the same question

1. Vector Functions and Space Curves a) Find the domain of the vector function: r(t) = (√4 – t², e−³t, ln(t + 1)) t² b) Find the limit: lime¯³ti + -j + cos 2t k sin² t t-0 c) Sketch the curve with the given vector equation. Indicate with an arrow the direction in which increases: r(t) = (sint, t)
Transcribed Image Text:1. Vector Functions and Space Curves a) Find the domain of the vector function: r(t) = (√4 – t², e−³t, ln(t + 1)) t² b) Find the limit: lime¯³ti + -j + cos 2t k sin² t t-0 c) Sketch the curve with the given vector equation. Indicate with an arrow the direction in which increases: r(t) = (sint, t)
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