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- Find y double prime using implicit differentiation5x^3+4y^3=11. Find the absolute maximum and minimum values of f(x)=10x(2-lnx) on [1,e^2] 2. Find the limil. Uisng L'Hopital's Rule : lim x arrow 0 sin^2(3x)/4x2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log (sin.π/x).?
- 4. If the secant method is used on f(x) = x^5 +x^3 +3 and if x_(n-2) = 0 and x_(n-1) = 1, what is x_n?Explain the following questions in detail how to solve with detailed Explanation. 1. Evaluate integral(upper limit=1/2 , lower limit=0) x4(1-2x)3dx using beta or gamma function.In 1934, the Austrian biologist Ludwig von Bertalanffy derived andpublished the von Bertalanffy growth equation, which continues tobe widely used and is especially important in fisheries studies. LetL(t) denote the length of a fish at time t and assume L(0) = L0. Thevon Bertalanffy equation isdL/dt = k (A - L),where A = limtSqL(t) is the asymptotic length of the fish and k is aproportionality constant.Assume that L(t) is the length in meters of a shark of age t years.In addition, assume A = 3, L(0) = 0.5 m, and L(5) = 1.75 m. Solve the von Bertalanffy differential equation.
- Solve for A and B so that F(x) has a limit at both x=2 and x=4A process creates a radioactive substance at the rate of 1 g/hr, and the substance decays at an hourly rate equal to 1/10 of the mass present (expressed in grams). Assuming that there are initially 20 g, find the mass S(t) of the substance present at time t, and find lim S(t) as t approaches infinity