Question 1 (25 Marks) a. Find the relative maximum and relative minimum points of the function,...
Problem 2: Find the Laplace transform of the following function f(t) = t3e2t + 2e-4t cos 4t + 5t2 sin 3t.
Question 4(25 marks) Find the critical points of following function, then determine whether they are relative maximum, relative minimum or saddle points i. f(x,y) 3x2-2xyy2- 8y [Smarks] [5marks] [5marks] iii. f(x,y)--2x + 4y-x2-4y2 + 9 b) Find the divergence and curl of the following vector fields i. F(x, y, z) = x2 yi + 2y3zj + 3zk [5marks] ii. F(x, y,z) x sin y i+4xyz j - cos 3z k [5marks]
Q1) Find the Laplace Transform of the following functions: 1. e +5 2. cos(2t)+7sin(2) 3t)+sin(3) 4. 10+ 5t +12-4 5. (+2)e 6. Gcos(21)-
6. Find the Laplace transform L{f} of the function f below. f(t) = 7t - sin(8t) + 3t cos(4t)
(4gts) Furst, consider the following two fanctions of time. Find the Laplace transform of each, and evaluate it at s = 4Hz F,(4Hz) ()-4 exp( -6)+5 cos(5t) 0-10 exp(-3t) cos(8t)+300 exp(-20) F,(4Hz) h Next, consider the following two functions of complex frequency s. Find the inverse Laplace transform of each, and evaluate it at 920ms 16 1(920ms) F,(6) s+4s + 68 16 400 200 d. F(s) S(920ms) (s+5y s+6 (You should enter at least 4 digits of precision for each....
) Find the Laplace transform of the following function f(t) = cos(5t) + t2-eat + 2
Find the Laplace transform F(s) L(f(t)) given f(t) = 5e-4 sin(5t) + 2e cos(6t). F(8) =
2. Find the Laplace transform of the following functions (a) f(t)3t+4 (b) cos(2Tt) (c) sin(2t T) (d) sin(t) cos(t) "Use Trig. Identity" (e) f(t) te 2t use first shifting theorem
(1 point) Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(t) = 5t? + 35t, g(t) = 5t2 – 35t NO_ANSWER 2. f(t) = edt cos(ut), g(t) = edt sin(ut) ,70 NO_ANSWER 3. f(x) = 51, g(x) = 5(2-3) NO_ANSWER 4. f(t) = 3t , g(t) = 1t|
Chapter 6, Section 6.2, Question 04 x Your answer is incorrect. Try again. Find the inverse Laplace transform L {F(s)} of the given function. 2s +12 F(S) = 2+12s+45 Your answer should be a function of t. Enclose arguments of functions in parentheses. For example, sin (2c). 2-'{F(s)} = 2e^(-3t)cos(6)