Solve the initial value problem for r as a vector function of t. dr 1 Differential Equation: t+ 1)'"?i+e ¯*j+ ´i+e¯j+- -k dt z(t+ 1) 2 t+1 Initial condition: r(0) = k %3D r(t) = (Di+ (Di+ Dk

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At time t=0, a particle is located at the point (3,9,4). It travels in a straight line to the point (7,8,6), has speed 6 at (3,9,4) and constant acceleration 4i-j+2k. Find an equation for the position vector r(t) of the particle at time t -O+¹+* The equation for the position vector r(t) of the particle at time t is r(t) = (Type exact answers, using radicals as needed.)

consider the vector-valued function r(t) = <2t3 – 15t2 + 36t, ln(4t – t^2)> a) State the domain of r(t) b) Identify where r(t) is not smooth over its domain. c) Identify any places where r(t) has vertical tangent lines. d) Identify any places where r(t) has horizontal tangent lines.

Format: Find the directional derivative of f(x, y, z) = -4x²z - 11 xy + 2z² at P = (-3, -3, -2) in the direction of (6,-2,0). D(6,-2,0)| (-3,-3,-2) O Search • If your answer below is a vector, input it as a column vector using the vector/matrix palette tool. • Use to explicitly indicate multiplication between variables and other variables, between variables and brackets, or between sets of brackets (e.g. x*y rather than xy; 2*(x+y) rather than 2(x+y)). . Put arguments of functions in brackets (e.g. sin(x) rather than sin x). . Give your answers in exact form. ab sin (a) Əə dx What is the maximum rate of increase of f at P? |Vƒl(-3,-3,-2) sin (a) Ә 2 f W ∞ f 8 a Ω a Ω Submit Assignment N Quit & Save [x] Back < 0 Question M 32 D

Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the equation r1(t)=r2(t) may not produce all the points where the graphs of these functions intersect.  Please Provide Unique Answer. Thank you!

Identify the minimum for the function using the vectoral application of Newton’s method while applying dynamic

A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)

Let R be a differentiable vector-valued function such that R'(t) = (3t2,2tvt? + 1, 2t + 3) and R(1) = (4, *2, 3). Find R(0).

Line A goes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A and passes through the point (6, 1, −3). Find a parametrization for each of the lines. (Use a different variable for the two parameters.)