Workshop #9 (Calculus III) | Answer Key - Edubirdie

University:
Seattle Pacific University
Course:
MAT 1236 | Calculus III
Academic year:

2024
Views:

388

Pages:

1
Author:

conget2w7

Workshop #9 1. The graph of ~r(t) = et ~i + e−t ~j is given. Carefully sketch ~r(t0 ) and ~r 0 (t0 ) for t0 = 0. 2. Find the parametric equations for the line that contains (2, −3, 1) and (5, 0, 4). Use your answer to give the parametric equations for the line segment that connects these points. D4 √ E 2 ~ , t + 2, 3t at the point (2, 2, 12). 3. Find the parametric equations for the line tangent to r(t) = t 4. Find the indicated derivative. D 1 E 2 (a) Find ~r 0 (t) if ~r(t) = cos(4t2 ), e4t , 2 4t √ 0 −1 ~ (b) Find ~r (2) if ~r(t) = tan (t) i + 3t2 + 4~j + ln(3t + 6) ~k 5. Evaluate the integral. Z t ~ 16t ~ (a) sec t tan t~i + j + e k dt 1 + t2 Z 1 t3 ~i + 1 ~j + te16t ~k dt √ (b) 1 + t2 1 + 4t4 0

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