determine f(x,t) for
0 < t
0 < x < 1
Determine f(x). f′′(x)=−cos(x)+sin(x), and f(0)=1, f(π)=0. Problem. f"(t) = -cos(T) + sin(), and f(0) = 1, f(1) = 0
dx Determine x= f(t) for (t? +4t) 4x + 4,t> 0; f(1) = 3. dt For (1? + 4t) dx dt = 4x +4, x= f(t) =
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
Please Write clearly Thank you x(t) ht) 2 2 2.12 Functions x(t) and h(t) have the waveforms shown in Fig. P2.12. Determine and plot y(t) = x(t) *h(t) using the following methods. (a) Integrating the convolution analytically. (b) Integrating the convolution graphically. h 0 0 t(s) t(s) 0 + 1 0 2 Figure P2.12: Waveforms for Problem 2.12.
QUESTION 11 Find the solution of x' + 2x' +x=f(t), x(0)=1, x'(o=0, where f(t) = 1 if t< 2; and f(t) = 0 if t> 2.
34.3 Let f be defined as follows: f(t) = 0 for t < 0; f(t) = t for 0 <t < 1; f(t) = 4 for t > 1. (a) Determine the function F(x) = $* f(t) dt. (b) Sketch F. Where is F continuous? (c) Where is F differentiable? Calculate F' at the points of differentiability.
x(0)=1, x'O)= 0, where f(t) = 1 if t< 2; and f(t) = 0 if Find the solution of X"' + 2x' + x=f(t), t> 2.
Given F(x, y) = (x²y3, xy). (a) Determine if F is conservative. If yes, find the scalar potential. (b) Evaluate F.dr where is the path defined parametrically by r(t) = (13 – 2t, t3 + 2t) e/F c for 0 < t < 1.
f(x+h)-f(x) 12. Determine lim h 0 h a. f(x)= x² answer: 2x 1 b. f(x)= x answer: 2√x c. f(x)=1/ x answer: -1/x? d. f(x)= et answer: et e. f(x) = sin x answer: COS X f. f(x)= = COS X answer: – sin x
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A, cos(nmi) +ΣB, sin (nπί), F(t)= Ao+ n1 n=1 (a) Sketch the function f(t) the function is even, odd or neither even nor odd. over the range -3<t< 3 and hence state whether (b) Calculate the constant term Ao Consider the periodic function defined by 1