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- Express the solution of the given initial value problem in terms of a convolution g(t) is an arbitrary function.2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?Solve the following initial value problem (t2-22t+105)(dy/dt)=y with y(11)=1 Find y as a function of t On what interval is the solution valid? Find the limit of the solution as t approaches the left and right ends of the interval
- Show that the solution of initial value problem: d^2x/dt^2 + w^2x = F0cosAt, x(0)=0, x'(0)=0 is x(t)= F0(cosAt-coswt)/(w^2-A^2). b) Evaluate lim,y>w F0(cosAt-coswt)/(w^2-A^2).Find the third iteration value of an extremum (maximum/minimum value) of if a = 5, b = 0.5, and c = 5 using Newton's Method with an initial guess value of x = - 4.3Find the third iteration value of an extremum (maximum/minimum value) if a = 4, b = 0.25, and c = 4 using Newton's Method with an initial guess value of x = -1.05 Round off the final answer to five decimal places but do not round off on previous calculations.
- 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.Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by N = 75 x - x^2Use differential approximations to estimate the increase in sales that will result by increasing the advertising budget from $10,000 to $10,850. Round to the nearest integer.________$ The total cost of producing a racket per hour is given by: C(x) = 0.53x²+4.6 x + 405 The average cost per racket at production level x rackets per hour is C'(x) = C'(x)/x Use differential approximations to estimate the change in average cost per racket if the production is increased from 20 per hour to 25 per hour. Round to the nearest cent.$_______per racket Yaster Electronics manufactures and sells æ televisions per month. The cost and revenue in dollars are given by C'(x) = 72,957 +59 x and R(x) = 204 x - 0.041 x2.Use differential approximations to estimate the change in profit if production level is increased from 1,500 to 1,559. Round to the nearest dollar. $________2. Approximate the root of the following function first using the bisection method and then using method of falsi position with the stopping condition |(x)| <8 x10^-4 .?(x) = x^3+2x^2+10x-20, [1, 2] .Which method converges faster to the solution?
- The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells in the blood. If S = k(H) = aHe-bH for positive constants a and b, with domain (0, infinity) and k'(H) = ae-bH(1-bH) 1. Use the definition to find the only critical point H1 of k on its domain. 2. Use a number line and the first derivative test to show that the oxygen supply is maximised at H1.You have to explain how you determine the sign of the first derivative on every interval. 3. What is the maximum oxygen supply? 4. How does increasing the value of the constants a and b in the same proportion change the maximumvalue of S? Please answer 3 and 413. Find the minimum and maximum value of the function on the giveninterval.y = 2x 2 + 4x + 5 [-2, 2]Consider the problem minimize 5x2+5y2−xy−11x+11y+11 (a) Find a point satisfying the first-order necessary conditions for a solution. b) Show that this point is a global minimum. c) What would be the rate of convergence of steepest descent for this problem? d) Starting at x=y=0, how many steepest descent iterations would it take (at most) to reduce the function value to 10−11?