Consider xy' = y(lnx-lny) with y(1) = 4. Using Runge-Kutta method with h=0.1, the k3 in the computation of y(1.4) is of the form In (). Compute In (+). B (a) - 0.77006 (b)-0.77600 (c) - 0.70706 (d) -0.70067
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- A polynomial of degree n I has exactly ____________________zero if a zero of multiplicity m is counted m times.If y = 5(1 - e-2x), compute y and show that y = 10 - 2y.Denote owl and wood rat populations in a particular area at time k by xk LK Rk where k is the time in months, Lk is the number of owls in the area studied, and R is the number (in thousands) of wood rats in the area studied. Suppose Lk+ 1 = (0.2)Lk + (0.6)Rk and Rk+1=(-0.1)Lk + (0.9)Rk. Determine the evolution of this system. (Give a formula for xk.) Does the owl population grow or decline? Does the wood rat population grow or decline?
- 5.3 Determine the real root of f(x) = -25 + 82x – 90x² + 44x³ – 8x* + 0.7x: (a) Graphically. (b) Using bisection to determine the root to ɛ, = 10%. Employ initial guesses of xị = 0.5 and x, = 1.0. (c) Perform the same computation as in (b) but use the false- position method and ɛ, = 0.2%.If L(x)=mx+b is the linearization of the cube root of 3x+1 at x=333 , then b= Enter your answer as a decimal. Use L(x) to approximate the cube root of 1003, the answer is Enter your answer as a decimal.Find the LCD of [(3/x + 1)and (5/x - 1)]
- The population P (in thousands) of a country can be modeled by P = −14.73t2 + 786.5t + 117,216 where t is time in years, with t = 0 corresponding to 1980. (a) Evaluate P for t = 0, 10, 15, 20, and 25. P(0) = thousand people P(10) = thousand people P(15) = thousand people P(20) = thousand people P(25) = thousand peopleSolve X(n) of the given X(z) using Residue MethodPROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4
- where did the 3/2 towards the end come from?If L(X)=mx+b is the linearization of the principal square root of x at x-900, then b- Use L(x) to approximate the principal square root of 903, the answer is Enter number as a decimal.3.8 (a) Evaluate the polynomial y = x' - 7x2 + 8x – 0.35 at x = 1.37. Use 3-digit arithmetic with chopping. Evaluate the percent relative error. (b) Repeat (a) but express y as y = ((x – 7)xr + 8)x – 0.35 - Evaluate the error and compare with part (a).