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7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t = 1): (a) Determine the domain of r. (b) Find lim r(t) if it exists. (You may use l'Hôpital's Rule.) t→1 What value (if any) could you give r(1) to ensure r is continuous at t = 1? (d) Find a tangent vector to r at t = 2. Write down a vector-valued function q(s) whose graph is the tangent line in (d).

7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t = 1): (a) Determine the domain of r. (b) Find lim r(t) if it exists. (You may use l'Hôpital's Rule.) t→1 What value (if any) could you give r(1) to ensure r is continuous at t = 1? (d) Find a tangent vector to r at t = 2. Write down a vector-valued function q(s) whose graph is the tangent line in (d).

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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How do I do d) and e)?

For d) I took the derivative of the vector r but I got a really weird solution which seems impossible

7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t ‡ 1): (a) Determine the domain of r. (b) Find lim r(t) if it exists. (You may use l'Hôpital's Rule.) t→1 What value (if any) could you give r(1) to ensure r is continuous at t = 1? (d) Find a tangent vector to r at t = 2. Write down a vector-valued function q(s) whose graph is the tangent line in (d).
Transcribed Image Text:7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t ‡ 1): (a) Determine the domain of r. (b) Find lim r(t) if it exists. (You may use l'Hôpital's Rule.) t→1 What value (if any) could you give r(1) to ensure r is continuous at t = 1? (d) Find a tangent vector to r at t = 2. Write down a vector-valued function q(s) whose graph is the tangent line in (d).
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