Answered: 5. Consider the following function:… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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5. Consider the following function: f(x) = xe - 1.
(a) (
) Find solution of f(x) = 0 up to 5 iterations using Newton's method starting with zo = 1.5. Keep
up to four significant figures.
(b) (
Consider the fixed point function, g(x) =
3
root must satisfy x = -
2
2x + 1
√x+1
Show that to be super-linearly convergent, the

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4. Consider the function, f(x) = x³ = x² - 9x +9. Answer the following: State the exact roots of f(x). (a) (b) Construct three different fixed point functions g(x) such that f(x) = 0. (Make sure that one of the g(x)'s that you constructed converges to at least a root). (c) (d) Find the approximate root, x, of the above function using fixed point iterations up to 4 significant figures within the error bound of 1 × 10-³ using xo = 0 and any fixed point function g(x) from part(b) that converges to the root(s). Find the convergence rate/ratio for g(x) constructed in previous part and also find which root it is converging to?
2. Determine the highest real root of f(x) = 2x³ - 11.7x² +17.7x-5 a. Graphically b. Fixed-point iteration method (three iterations, xo =3). Note: Make certain that you develop a solution that converges on the root.
2. (b) Suppose instead that the true speed of the car as a function of time is described by v(t) = 30√t (still from t = 0 to t = 4). Sketch a graph of the car’s speed vs. time. (c) Since the speed is no longer constant, it is much harder to calculate the distance traveled. But we can still try. Suppose we wanted to just calculate how far the car went in the single minute from 1:00 and 1:01. Let’s pretend that the car’s speed is constant for this single minute. What might be a reasonable approximation for the car’s speed, in this scenario? Under this assumption, approximately how far did the car go during this minute? Represent the distance traveled during this one minute as an area in your diagram from part (b).
A company is producing a new product. Due to the nature of the product, the time required to produce each unit decreases as workers become more familiar with the production procedure. It is determined that the function for the learning process is T(x)=2+0.3(1/x),where T(x) is the time, in hours, required to produce the xth unit. Find the total time required for a new worker to produce units 1 through 10; units 20 through 30.
Consider the following equation f(x) = x³ – 3x2 + 3x- 1= 0, [0.5, 1.5] | Determine a function g(x) on which fixed point iteration will converge to appositive .solution of the equation (Prove that g(x) will converge) b. Find the solution (to P4)
A tank contains 1000-gallon of pure water. Starting at time t = 0, a solution containing 0.2 lb of salt per gallon enters 10 gallons per minute and the well-stirred solution is withdrawn at a rate of 5 gallons per minute. Set up the initial value problem for the amount of salt, Q(t), in the tank as a function of t. Sove for Q(t).
Most functions can be rearranged in several ways to give x = g(x) with which to begin the fixed-point method. For f(x) = e² – 2x² = 0, one g(x) is ex x = ±. 2 (a) Show that this converges to the root near 1.5 if the positive value is used and to the root near -0.5 if the negative is used. (b) There is a third root near 2.6. Show that we do not converge to this root even though values near to the root such as p. o = 2.5 or p, = 2.7 are used to begin the iterations. (c) Find another rearrangement that does converge correctly to the third root.
identify the coordnates of any local maximum or minmum values of the function y=(x+3)2/ e2x
2. The Batmobile travels in a straight line such that t seconds after passing through Arkham, its velocity v(t) in meters per second is given by v(t) = 5t3 + (20 – 30k)t² – 100kt + 200k + 50 where k is constant. (a) Find an expression for the acceleration of the Batmobile in terms of k and t. (b) Suppose that the acceleration of the Batmobile five seconds after passing through Arkham is 175 m/s?. Determine the value of k five seconds after passing through Arkham. (c) Using the value of k from item (b), find the range of values of t for which the Batmobile is accelerating positively. (d) Using the value of k from item (b), determine the values of t when the Batmobile is accelerating at its fastest and slowest within six seconds of passing through Arkham.
Ex 6. Find the points at which the given function f has a local extremum: (i) f(x)=x²-11 on I = [-4,4]. (ii) f(x) = xr² - 12 on I = [-2,3]. (iii) f(x) = x(x-8)1/3 on I = [0,9].
3.) Determine the root of the equation by Secant Method (should converge at three decimal places a.) k(x) = In(x³)-5, xa=6.1, x,=5.5
Assume that it costs that same company approximately C(r) =67,822+4,195z+0.05z2 dollars to manufacture r of their new and improved deluxe game play stations in an hour. Find the average cost function, C(2), and use it to find the average cost, per deluxe game play stations to produce the first 1,311 deluxe stations rounded to the nearest cent (that is two decimal places).

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