1. (15 points) Consider the vector-valued function $$r(t) = t^3i + e^tj - 2k$$. Then $$\lim_{t\to 0} r(t)$$ is O j - 2k O $$3t^2i + e^tj - 2k$$ O 0 O -1 O none of the above 2. (15 points) The distance between the points
Added by Robert B.
Close
Step 1
$$r(t) = t^3i + e^tj - 2k$$ $$\lim_{t\to 0} r(t) = \lim_{t\to 0} (t^3i + e^tj - 2k)$$ Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 55 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
25. r(t) = ln t i + (t - 1)/(t + 2)j + t ln t k, t0 = 1 26. r(t) = (cos t)i + (sin t)j + (sin 2t)k, t0 = pi/2 In Exercises 27–30, find the value(s) of t so that the tangent line to the given curve contains the given point. 27. r(t) = t^2i + (1 + t)j + (2t - 3)k; (-8, 2, -1) 28. r(t) = ti + 3j + (2/3 t^(3/2))k; (0, 3, -8/3) 29. r(t) = 2ti + t^2j - t^2k; (0, -4, 4) 30. r(t) = -ti + t^2j + (ln t)k; (2, -5, -3)
Sri K.
Find the parametric equations that correspond to the given vector equation. r = (12t - 1)i - 7∑tj + sin 11tk x = y = z = Find the limit. lim (t -> 5) (ti - 3j + t^2k) lim (t -> 5) (ti - 3j + t^2k) = i + j + k Find parametric equations of the line tangent to the graph of r(t) at the point where t = t0. r(t) = t^2i + (4 - ln t)j; t0 = 8 x = y = Evaluate the indefinite integral. ∫(7i + 10tj)dt = i + j + C
Madhur L.
Chapter 12 1) Let r(t) = (ln t)i + e^-3t j + t^2 k Then r''(t) = -1/t^2 i + 9e^-3t j + 2k True False 2) The function g(t) = (cos t)i + (sin t)j + ⌊ t ⌋ k is discontinuous at every integer, ⌊ t ⌋ is the greatest integer function. True False 3) Find r(t) ∙ (r'(t) × r''(t)) Given the vector-valued function r(t) = i + tj + t^2 k
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD