Problem 2: For each of the following functions find
f'(x)
Problem 2: For each of the following functions find f'(x) Problem 2 (20 points): For each...
(15 points) Find the derivative of the following functions. You do not have to simplify answers. ecos (22+2+1) 1. (5 points) f(x) = 2. (5 points) g(x) = So" con (+0+1)dt + So sin tdt 3. (5 points) h(x) = Licen (o? +++ 1)dt
problem 7
Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure. 2: Triangular Function Problem-5 [10 Pointsl A system has the transfer function h(s) = (s1)(s +2) a) Find the impulse response of the system b) Determine the output y(t), given that the input is x(t) u(t) Problem-6 [10 Pointsl Use the Laplace transform to solve the differential equation +22+10v(t) 3 cos(2t) dt2 dt subject to v(0)-1, dv(O) Problem-7 [10 Points] Solve the integrodifferential equation...
6 A Find the derivative of each of the following functions using derivative rules. Remember to SIMPLIFY first! Show all steps for full marks <2 mks each> Differentiate each of the following equations. Be sure to write proper notation. y = 7x6 + 10x4 - 8x - 5 $(x)= V1 f (x) = 7 y = 4x®(3x6 - 2x) f (x) = - s(t)= _4° +56 f(x)g(x)h(x) cf(x) f(x) + g(x)
Prob.II. Differentiate the following functions, and simplify. 1. f(x) 2x-3 x+4 2. f(x) = x²(x - 2)* 3. f(x) = In (x V1 - x2) 4. f(x) = x2e-* 5. Find dy/dx = y' for the equation x2 + y2 = 25 and find y" (check H.W)
(x)). For each pair of functions f and g below, find f(g(x)) and g Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) f(x) = x + 4 (b) f(x) = - -, 0 3x x 5 ? g(x) = x - 4 f(g(x)) = 0 8(x)...
For f(x) = 2-x and g(x) = 2x2 +x+6, find the following functions. a. (fog)x); b. (gof)(x); c. (fog)(2); d. (gof)(2) a. (fog)(x) = 0 (Simplify your answer.) b. (gof)(x) = 0 (Simplify your answer.) c. (fog)(2)- d. (gof)(2)-
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For f(x) = 2x and g(x)= x + 2, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(3); d. (gof)(3) a. (fog)(x) = (Simplify your answer.) b. (gof)(x) = 0 (Simplify your answer.) C. (fog)(3) = d. (gof)(3)=0
For each pair of functions f and g below, find f(g(x)) and g(x)). Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) f(x) = -,x0 (b) f(x) = x + 4 $(x) = -,x+0 x 5 ? g(x) = -x + 4 $($(x)) = 0 (g(x)) =...
For f(x) = Vx and g(x) = x + 7, find the following functions. a. (f o g)(x), b. (g o f)(x), c. (f o g)(2), d. (g o f(2) a. (fo g)(x) = L」 (Simplify your answer.) b. (gof)(x)=[-] (Simplify your answer) C. (fog)(2)-O (Simplify your answer) d. (g o f(2)- (Simplify your answer)
problem 6
(1 point) Finding Equations of Exponential Functions For each of the following, find the formula for an exponential function that passes through the two points given a. (0, 2) and (4, 1250) f(t) = b. (0,12500) and (4, 20) g(x) =