Question 1 1.67 pts The function F(t) is an antiderivative of f(t) = (0.95). Choose the...
(1 point) Consider the function f(t) = 10 sec?(t) – 6t". Let F(t) be the antiderivative of f(t) with F(0) = 0. Find F(t).
The sketch of the following periodic function f (t) given in one period f(t) t2 -1, 0s t s 2 is given as follows f(t) 2 -1 We proceed as follows to find the Fourier series representation of f (t) (Note:Jt2 cos at dt = 2t as at + (a--)sina:Jt2 sin at dt = 2t sin at + sin at. Г t2 sin at dt-tsi. )cos at.) Please scroll to the bottom of page for END of question a) The...
Consider the function f(t)=10sec^2(t)−3t^3 Let F(t) be the antiderivative of f(t) with F(0)=0. Then F(t)=...
Question 9 3 pts The Laplace transform of the piecewise continuous function 4, 0<t <3 f(t) is given by t> 3 (2, L{f} = { (1 – 3e-*), s>0. O 2 L{f} (2 - e-st), 8 >0. 2 L{f} = (3 - e-st), s >0. O None of them 1 L{f} (1 – 2e -st), s >0.
For the following function f, find the antiderivative F that satisfies the given condition. л T 5 f(v)= = sec v tan v, F(0) = 4, 6 2 2 F(v) = AY Use the figures to calculate the left and right Riemann sums for f on the given interval and the given value of n. f(x)= 3- 3- xi'w 3 f(x) = on (1,5); n = 4 X х 4 5 0 1 4 5 The left Riemann sum for...
Question 2 (3 marks) Function f(t) is described as a sudden change of 1 SI unit at t-0 followed by a sudden change of -1 SI unit after 0.2 seconds. Assume f(t)-0 for t<0. (a) Write the analytical form of f(t). Sketch its graph indicating clearly all relevant values. (b) Find the Laplace transform of f(t) (c) Derive the expression for F, (s) if f(t) f(t)dt (d) Please see over
Question 2 (3 marks) Function f(t) is described as a...
Question 48 1.67 pts When people decide to spend a smaller percentage of each paycheck, this causes national saving to closed economy and the equilibrium interest rateto_Ina Increases increase decrease increase decrease decrease Increase decrease Ned < Previous Not ved Submit 30 SO 9 & 7 8 $ 4 % 5 # 3 6 2 P U Y T R W E к J H G F. D S N M B V C X Question 49 1.67 pts Fluctuations...
Let f(t) be a function on [0, 0). The Laplace transform of f is the function F defined by the integral F(s) = e-stf(t)dt. Use this definition to determine the Laplace transform of the following function. 0 est 0<t<1 f(t) = 1 <t for all positive sand F(s) = 1 + 5 -5 otherwise. The Laplace transform of f(t) is F(s) = (Type exact answers.)
(1 point) Consider the function f(x) = f* cos(t) – 1 dt. t2 Which of the following is the Taylor Series for f(x) centred at x = 0? w A. (-1)" (2n – 1)(2n)! -x2n- +C. n=0 (-1)"(2n – 2) 2n–3. B. (2n)! n=1 c. Σ (-1)" (2n + 1)! -x2n-2 n=1 D. Š (-1)" -X2n-1 (2n – 1)(2n)! n=1
Elementary Laplace Transtorms Y(S) = {f} -L e-stf(t)dt fc = C-'{F(s)} F(s) = {f} f(t) =-'{F(s)) F(s) = {f} -CS 1. 1 1 12. uct) le S> 0 S> 0 . s S 2. eat 1 13. ucOf(t-c) e-csF(s) S> a S-a n! 3. t",n e Z 14. ectf(t) F( sc) S> 0 sh+1 4. tP, p>-1 (p+1) S> 0 SP+1 15. f(ct) F). c>0 16. SFt - 1)g(t)dt F(s)G(*) 5. sin at S> 0 16. cos at 17. 8(t...