Consider xy' = y(lnx-lny) with y(1) = 4. Using Runge-Kutta method with h=0.1, the k² in the computation of y(1.4) is of the form In (). Compute In() (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.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.
- 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?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.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 people
- PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 45.3 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%.Consider f(x) = 6x + 3 and g(x) = x² – 2x – 48. • You must combine all like terms before you submit your answer. • You must expand all products before your submit your answer. a. Compute: (f o g)(3) = b. Compute: (go f)(3) = c. Compute: (f o g)(-2) = d. Compute: (go f)(-2) = e. Simplify: (fo g)(x) = f. Simplify: (go f)(x) :
- The population P (in thousands) of a country can be modeled by P = -14.79t² + 786.5t + 117,228 where t is time in years, with t = 0 corresponding to 1980. (a) Evaluate P for t = 0, 10, 15, 20, and 25. thousand people thousand people thousand people thousand people thousand people P(0) = P(10) P(15) P(20) P(25) = Explain these values. The ---Select--- = dp dt = = (b) Determine the population growth rate, dp/dt. (c) Evaluate dp/dt for the same values as in part (a). P'(0) = thousand people per year thousand people per year thousand people per year thousand people per year thousand people per year P'(10) P'(15) = P'(20) P'(25) = is ---Select--- = Explain your results. The ---Select--- is ---Select--- ✓Solve X(n) of the given X(z) using Residue Method