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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 ft) be a function on [0, đo). The Laplace transform of f is the function F defined by the integral F(s) = f' e - stf(t)dt. Use this definition to determine the Laplace transform of the following function. 0 est 0<t<3 f(t) = 4, 3<t 4 15 e otherwise. The Laplace transform of f(t) is F(s) = 3) = for all positive stand F(s) = 3 + (Type exact answers.)
5pt 1. Let g() = | f(t) dt, where f is the function whose graph is shown below on the interval [0, 5). The graph consists of two straight line segments. - - - ------ -1- - - - - - --1- - -1- - - - - - - (a) Find g(1) and g(3). (b) On what interval(s) is g(x) decreasing? (c) At what x-value(s) in (0,5) does the local maximum of g occur? (d) At what x-value(s) in...
Let f(t) be a function on [0, 0). The Laplace transform of fis the function F defined by the integral F(s) = estf(t)dt. Use this definition to determine the Laplace transform of the following function. 3 0<t<2 5. 2<t *** The Laplace transform of ft) is F(s) = { for all positive s+ and F(5)=2+ c otherwise (Type exact answers.)
1.(4 pts) A rectangular tank, shown in Figure A, is 4 ft long, 2 ft wide, and 3 ft high. Initially there is 4 fts of water in the tank and water starts flowing into the tank at the time t Let V (t) denote the volume of the water in the tank at the time t. The graph of V', the derivative of V, o ft3 is given in figure B, where t is in minutes, and V'in min...
Let f(t) be a function on (0, 60). The Laplace transform of f is the function F defined by the integral F(s) = 5 e - str(t)dt. Use this definition to determine the Laplace transform of the following function. 0 9-t, 0<t<9 f(t) = 9<t for s# The Laplace transform of f(t) is F(s) = (Type exact answers.) 81 and F(s) = otherwise. 2
Let f(t) be a function on (0, 60). The Laplace transform of f is the function F defined by the integral F(s) = 5 e - str(t)dt. Use this definition to determine the Laplace transform of the following function. 0 9-t, 0<t<9 f(t) = 9<t for s# The Laplace transform of f(t) is F(s) = (Type exact answers.) 81 and F(s) = otherwise. 2
(1 point) Let F(x) = [” f(e) dt, where f(t) is the graph in the figure. Find each of the following: A. F(3) = B. F'(5) = C. The interval (with endpoints given to the nearest 0.25) where F is concave up: 1 2 4 6 7 interval = (Give your answer as an interval or a list of intervals, e.g., (-infinity,8] or (1,5),(7,10), or enter none for no intervals.) D. The value of x where F takes its maximum...
Let f(t) be a function on (0.00). The Laplace transform of fis the function F defined by the integral F(s) = -La e-stf(t)dt. Use this definition to determine the Laplace transform of the following function. le 21 Oct<3 FCU = 4 3<t -6 otherwise The Laplace transform of ft) is F(s)- for all positive s# and F(s) = 3 +2 e (Type exact answers.) Enter your answer in each of the answer boxes.
Let f(t) be a function on [0, 0). The Laplace transform of f is the function defined by the integral Foto F(s) = e - st()dt. Use this definition to determine the Laplace transform of the following function. 0 e2t, 0<t<3 f(t) = 3<t for all positive si -6 and F(s) = 3+2 e otherwise. The Laplace transform of f(t) is F(s) = (Type exact answers.)