Find f. f'(t) = 2t - 4 sint, (0)= 5 Select one: a. f(t) = 2t - 3 sint +5 O b. f(t)= +2 +4 cost +1 c. f(t)=12 - 3 cost-5 d. f(t) = x2 +3 cost e. None of these
Find a parametrization of the tangent line at the point indicated. r(t) = <1 − t4, 2t, 3t3> t = 2 L(t) = <−23t−15,2t+4,36t+24>
You must show your work clearly!!! Let W W t0) be a Brownian motion. Find E(W (W14 t+4 Wt15)): Select one: t2 3 2t 3 x 2t Let W W t0) be a Brownian motion. Find E(W (W14 t+4 Wt15)): Select one: t2 3 2t 3 x 2t
Let f(t) = 2t + 4. f-1(s) Let g(x) 2 + 1 g-(3) Below is an input-output table for the function h(x). х h(x) 2 0 1 1 2 الها 3 1 4 0 h-(3) = Now consider the following graph: 5 3 2 -5 -4 -3 -2 -/ 2 Cat 3 4. -2 3 -4 -5+ q
dan Multiplication by t. 8. Find the following Laplace transforms using the formula L[t"f(t)] = (-1)", (a) [t3e-36] (b) C[(t + 2)2e'] (c) C[t(3 sin 2t - 2 cos 2t)] (d) L[tsin t] (e) C[t cosh 3t) (1) [(t-1)(t - 2) sin 3t] (g) [t3 cost] 9. Applying L[t"f(t)] = (-1)", , calculate (a) Sºte-3t sin t dt (b) Scºt?e-t cost dt recimento e contato Llegarsim 225 (-1)" IEC d'Fs) dsh
' cos(3t), t<n/2, 2. Let f(t) = sin(2t), 7/2<t< , Write f(t) in terms of the unit step e3 St. function. Then find c{f(t)}.
Let α = {1 + 2t, t − t 2 , t + t 2} (a) Show that α is a basis for P2(R). (b) Let p(t) = 1 + 3t + t 2 . Find [p(t)]α. (c) Define the transformation T : P2(R) → P2(R) as T (p(t)) = p 0 (t) − p(t) i.e., the difference of p(t) and its first derivative. Determine whether this transformation is a linear transformation. (d) Find [T]α Problem 4. Let a =...
all parts -2t e - (13 points) Let f(t) cos 2t, sin 2t) for t 2 0. F() (a) (4 points) Find the unit tangent vector for the curve d (F(t)-v(t)) using the product rule for dt (b) (5 points) Let v(t) = 7'(t). Calculate the dot product and simplify v(t) (c) (4 points) For an arbitrary vector-valued function 7 (t) with velocity vector = 1, what can be said about the relationship between F(t) and v(t)? if F(t) (t)...
1. Find the Laplace transform of the function f(t) = 1 + 2t + 3e-3t - 5 sin(4t). Solution: 2. Find the inverse Laplace transform of F(s) = 7+ (8 + 4)(18 - 3s) (s - 3)(s – 1)(s + 4)" Solution:
2, let f(t)-〈 2t 2-t < 4 ; g(t) = . 0 otherwise 0 5<t (a) Write each function in terms of the unit step fun ction (b) Plot each function (c) Find the Laplace transform of f (t) and g(t) 2, let f(t)-〈 2t 2-t