Find destr(e) • u(e)] and cr(e) * u(t)] in two different ways. r(t) = cos ti...
(1) 8ketch the graph of r(t) and show the direction of increasing t 2:r, c) r(t) -3costí + 3 sin tj + tk; d) a) r(t).-ti+3, b) r(t)-< 2cos t, 5 sin t >, О r(t)- ti+ t2j + 2k t Describe the graph of r(t) 3 cos ti+5sin tj+4 cos tk (1) 8ketch the graph of r(t) and show the direction of increasing t 2:r, c) r(t) -3costí + 3 sin tj + tk; d) a) r(t).-ti+3, b) r(t)-,...
Let u(t)= ti+ln(t)j + et k and v(t) = ti+2tj+1k. Compute the derivative of the dot product [u(t)- v(t)] in two ways and confirm they agree: • Compute the dot product u(t). v(t) first and then differentiate the result. • Alternatively, use the following “Dot Product Rule" v(t)] = u'(t) . v(t) + u(t) . v'(t). (1)
Solve for 14(b,c) and 18 (b,c) please 16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the graph of r(t) (e.2 cos(t).2sin(t)) at to-0. Use the qu tion to approximate r(0.1). tion function to find the velocity and position vectors at t 2. 17. Find the principal unit normal vector to tih curve at the specified value of the parameter v(0)-0, r(0)-0 (b) a(t)cos(t)i - sin(t)i (a) r(t)-ti+Ij,t 2 (b) rt)-In(t)+(t+1)j.t2 14. Find the...
Find the tangential and normal components of acceleration of a particle with position vector r(t) = 4 sin ti + 4 cos tj + 3tk.
Let u(t) =t^3 i + ln(t) j + e^2t k and v(t) = 1/t^3 i + 2 j + t k 2. Let u(t) - ti+In(t)j+ et k and Compute the derivative of the dot product f u(t)v() in two ways and confirm they agree: Compute the dot product u(t) v(t) first and then differentiate the result. . Alternatively, use the following "Dot Product Rule" u(t) v(t)] u'(t) v(t)+ u(t) v'(t) Aside: It's worth noting that there are other forms...
Choose the graph that matches the vector equation. r(t) = – ti + tj + tk, Osts 1 Choose the correct answer below. A. B. C. D. Az AZ (-1, 1, 1) (1, 1, 1) 1 A у X X X |(1, 1, -1) X
In the previous homework, the Fourier Transform of x(t)- t[u(t)-u(t-1) was found to be x(t) 2 0 -1 -2 -3 5 4 3-2 0 2 3 4 5 a) b) Using known Fourier transforms for the terms of y(t), find Y(j). (Hint: you will have to apply some c) Apply differential properties to X(ju) to verify your answer for part b Differentiate x(t), y(t) = dx/dt. Note, the derivative should have a step function term. Include a sketch of y(t)...
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y + sin(40k. (b) Find the unit tangent vector at the point t0. SOLUTION (a) According to this theorem, we differentiate each component of r: t 45 cos (4t) r(t) + 3 (b) Since r(0)= and r(o) j+4k, the unit tangent vector at the point (3, 0, 0) is i+ 4k T(0) = L'(0)-- EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y +...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
arosinu+rvi-r)for-1 < u < 1 and (r+1 cos ur+1 sin u, Let x(u, e) 9. = (a) Compute the first fundamental form of S (b) Compute the Christoffel symbols of S (c) Compute the Gaussian curvature of S (d) For which to is the curve a(t) = x(t,%) a godesíc. arosinu+rvi-r)for-1