HER Question 1 Calculate - [11 (1) r2(1)] and dr [r(1) r2(0] first by differentiating the...
Calculate [rı(t) r2(0)] and — [rı(t) x r2(0)] first by differentiating the product directly and then by applying the following formulas: dt dri dr2 [ri(t) r2(0)] = r1(t). dt dt + . r2(t) dt dr2 [ri(t) x r2(t)]=rit) x dt + dri Xr2(t) dt ri(t) ) = cos ti+ sin tj + 5tk, r2(t) = 4i+ tk Enter the vector i as 7, the vector jas į , and the vector k as R. [rı(t) · r2(0)] = ? Edit...
Question 1 d Calculate — [rı(1). 120] and — [rı(1) Xr2O] first by differentiating the product directly and then by applying the following formulas: dt d - [ri(t) r2(]=r(t) dt d r2 dri + - rz(t) dt dt dr2 dri -+- Xr2(1) dt dt d [rı(t) x r20]=r10) dt ri(t) = = cos ti + sin tj +6tk, r2(t) = 5i + tk Enter the vector i as 7, the vector j as 7, and the vector k as K....
QUESTION 1 Find r' (3) if r(t) = t3i+tj + tk A. 3i + 2+ 1k B. 18 i +6j+1 k C. 9 ii+ 3j+0k D. 27 i +6j+1 k QUESTION 2 Find r' (11/2) if r(t) = 2sin(t) i + 3cos(t)j OA. -2 i + Oj 01 – 3j c.2 i + 3j D. 01 + 1 j QUESTION 3 Evaluate S 3421- 4 të jdt A. 31 - 4j i cu B.31 +4j cli - 1j Da bit...
1 a) Find the domain of r(t) = (2-Int ) and the value of r(to) for to = 1. b) Sketch (neatly) the line segment represented by the vector equation: r=2 i+tj; -1 <t<l. c) Show that the graph of r(t) = tsin(t) i + tcos(t) j + t?k, t> 0 lies on the paraboloid: z= x2 + y². 2. a) Find r'(t) where r(t) = eti - 2cos(31) j b) Find the parametric equation of the line tangent to...
question 2 in two parts Incorrect Question 2 0/1 pts The first question in this problem is "How fast is the radius of the balloon changing at the instant the balloon's diameter (dis 12 inches?" Which of these sketches best records the known and unknown quantities that are relevant to this question? dr/dt? d=12 dv/dt=20 r=6 d=12 dv/dt=20 =6 dr/dt=20 d=12 r=6 dr/dt=20 dv/dt = ? d=12 Incorrect Question 3 0/1 pts Part b of Preview Activity 3.5.1 reads: "Recall...
QUESTION 4 Given the equation of a point, r(t) ( I)i ( -I)j Sketch the graph of r(r) = (1 + l)i + (r2-Dj fr-2 2. Draw the (a) t 4 marks) position vector r(0) on the same diagram. b) Find the unit tangent vector of the point at 0 and show it on the same diagram in (a). Explain what you understand about the direction of the tangent (5 marks)
R 1 (1) L + us(t) = u(1) v (0) R2 } v. (!) (t) + 20%*(t) + war(t) = f(t). Let x(t) be volt). (a) Determine iz(t). Hint: Apply Ohm's law on R2. (b) Determine dir()/dt. (c) Determine u(t). (d) Determine vct) using KVL. (e) Determine current through Ry using KCL. (f) Determine vs(t). (g) Determine a and wo.
Question 1. If C is a smooth curve given by a vector function r(t), a stsb, show that Ser-dr = žlır(b)l2 – Ir(a)i?) Hint 1: Use the product rule and the fact that the dot product is commutative (this means a b = b.a for any two vectors a and b) to write: r(t).r' (t) Hint 2: Use FTC2 from first year calculus. 1 d 2 dt
Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of continuous functions from [0, 1 to R equipped with the usual function addition and scalar multiplication, is a vector space. (b) Let (V, K, +,-) be a vector space. Show that a non-empty subset W C V which is closed under and - necessarily contains the zero vector. (c) Is the set {(x,y)T: z,y E R, y a subspace of R2? Justify.
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...