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- y = (4 + x)-¹/2, Find the Linearization L(x) = = a = 5 at x = a.Find the linearization L(æ) of the function g(æ) = xf(x²) at æ = 2 given the following information. f(2) = 0 f'(2) = 10 f(4) 5 f'(4) = -3 Answer: L(x)If s(t) = 4t– 6t - 24t + 5, represent the position of a particle traveling along a horizontal line. Determine the time intervals when the object is slowing down or speeding up from the velocity and acceleration %3D functions. O speeding up in (-o,0.5) U (2, 00)and slowing down in (5, o0) speeding up in (-∞,0.5) U (2, 0)and slowing down in (0.5, o0) speeding up in (-0,0.5) U (2, 5)and slowing down in (0.5, 2) speeding up in (-0,0.5) U (2, 0) and slowing down in (0.5, 2) O speeding up in (-∞,0.5) N (2, 0)and slowing down in (0.5, 2)
- The Lotka-Volterra equations are often used to model the links between a particular population of prey organisms and a population of predatory organisms. In a particular ecosystem u is used to represent the number of predatory organisms and v to represent the number of prey organisms. Suppose the growth rate uv of the predatory organisms is f(u,v) = - 0.5u + and of the prey organisms is g(u,v) = 6v – 10uv. 100 (a) Show that if u = 0.6 and v = 50, then f (u,v) = 0, and g(u,v) = 0. (The populations are said to be in equilibrium.) %D %3D f(u,v) (b) Find the linear approximation of the vector valued function h:(u,v)→ if u is close to 0.6 and v is g(u,v) close to 50. (a) Evaluate f(u,v) at u = 0.6 and v = 50, f(0.6, 50) = (Type an integer.)A bank saving account with a fixed interest rate is modeled using the following difference equation: y[n]- y[n- 1]-rx y[n– 1]= x[n] where r is the interest rate per month. A person opens a new saving account and deposits $1,500 to his/her saving account in the first day (i.e., x[0]=$1,500) and do not deposit any more money after that. If we assume that the interest rate is 0.5%, show that the amount of money in the account at the 3rd month (n=3) is approximately $1,522.61.In the xy-plane, the graph of a linear equation of the form y = mx + b and the graph of an exponential equation of the form y = ab* both contain points (1, 3) and (2, 4). If the point (r, s) is on the graph of the linear equation and the point (r, t) is on the graph of the exponential equation, where 0 t, which of the following must be true? (A) 0