
(1 point) Let f(x) = [: to dt. Evaluate the following. f'(x) = f'(5) =
Find the time constant t of the following differential
equation: a(dy/dt)+by+cx=e(dx/dt)+f(dy/dt)+g, of the given that x
is the inout, y is the output, and a through g are constants.
13, Find the time constant τ from the following differential equation, dt dt given that x is the input, y is the output and, a through g are constants. It is known that for a first-order instrument with differential equation a time constant r- alao dy the
13, Find the time...
Let F(x) = Sý sin*(0) dt. Evaluate the following limit . Let F(x) = $* sin?(t) dt. Evaluate the following limit. 2022
(Problem 3) Consider the following three-species ecosystems: dF F(a – cS) dt ds S(-k + \F – mG) dt dG G(-e+oS). dt Assume that the coefficients are positive constants. Describe the role each species plays in this ecological system. =
Find the following integrals using integration by parts (IBP)
(e) cos'(t)dt (f) S[In(t)]?dt (g) 83" 02 sin(20)de
f'(x) if f (x) = Sỉ tsin(3t)dt.
6. If f(x) = 5,*v2 dt, then f'(3) is:
Let F(x) = f f (t) dt for 2 in the interval (0,3), where f (t)is the function with the graph given in the following diagram. Ne 1 37 - 1 -2 Which of the following statements are true? Select all that apply. Fhas a local maximum at 2. F has a local minimum at 2. F is increasing on the intervals (0,0.5) and (2.5, 3). Fis decreasing on the interval (1.5, 2.5).
Let S f(w)dt = 6, f(x)dx = -4, log(x)dt = 12, 9(x) dx = 9 Use these values to evaluate the given definite integral: -3 (f(x) f(x) + g(x)) dx
at the end of the day $443 in cash is in there registered in the amount of the change fund is $100 if the cash register tape indicates $345 which of the following journal entries should be made