Consider the equation xln(x)= 1 for x≥1. In this problem, you are asked to show that...

Consider the equation xln(x)= 1 for x≥1. In this problem, you are asked to show that this equation has a unique solution 1≤x <∞by completing both parts below. Note that you are not asked to find this solution, just to show that it exists and that it is unique!

(a) Show that the equation has at least one solution x such that 1≤x <∞.

(b) Show that the equation has at most one solution x such that 1≤x <∞.

Expert Solution

milcah answered 2 years ago

1. In this problem, you are asked to consider cases in which “more is not better.”...

1. In this problem, you are asked to consider cases in which “more is not better.” For each of the following scenarios, draw an appropriate indifference curve map over different combinations of Brussels sprouts (X) and broccoli (Y). Put Brussels sprouts (X) on x-axis and broccoli (Y) on Y-axis. Draw 3 indifference curves for each scenario and labeled, , and , from the lowest to the highest utility level. Hint: to determine the slope of the indifference curves, i.e. whether...

5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not...

5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not exact. (b) Find a value for the constant a such that, when you multiply the d.e. through by xa, it becomes exact. Show your working. Do NOT solve the resulting differential equation. 6. Consider the differential equation (D − 3)(D − 4)y = 0. (a) Solve this d.e., showing brief working. (b) How many solutions does this d.e. have? Justify your answer. (c) How...

a) Consider a plane strain formulation. Show that the plain strain problem satisfies the following equation:...

a) Consider a plane strain formulation. Show that the plain strain problem satisfies the following equation: ??(?? + ??) = −?/? − ? (???/?? + ???/??) b) Consider a plane stress formulation. Show that the plain stress problem satisfies the following equation: ??(?? + ??) = −(? + ?) (???/?? + ???/??) (Hint: You may use the equations given below ?????? ∶ ??? = ??,? + ??,? ??????: ??? = 2???? + ??????? ?????? ???????????: ???,? + ?? = 0...

Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where...

Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where x=[x(t)y(t)]. x(t)= y(t)= please be as clear as possible especially when solving for c1 and c2 that's the part i need help the most

In the problem, you are on a game show, being asked to choose between three doors....

In the problem, you are on a game show, being asked to choose between three doors. Behind each door, there is either a car or a goat. You choose a door. The host, Monty Hall, picks one of the other doors, which he knows has a goat behind it, and opens it, showing you the goat. (You know, by the rules of the game, that Monty will always reveal a goat.) Monty then asks whether you would like to switch...

Use Rolle’s Theorem to show that the equation ln(1 + x 2 ) + 2x =...

Use Rolle’s Theorem to show that the equation ln(1 + x 2 ) + 2x = 0 has at most one solution. Provide a full explanation, justifying each step in your argument.

1). Consider the quadratic equation x^2+ 100 x + 1 = 0 (i) Compute approximate roots...

1). Consider the quadratic equation x^2+ 100 x + 1 = 0 (i) Compute approximate roots by solving x^2 -100 x = 0 (ii) Use the quadratic formula to compute the roots of equation (iii) Repeat the computation of the roots but use 3 digit precision. (iv) Compute the relative absolute errors in the two 3 digit precision root approximations in (iii). (v) With x1 =1/2a (-b + sqrt b^2 - 4ac and x2 = 1/2a (-b + sqrt b^2...

(a) Consider the function f(x)=(ex −1)/x. Use l’Hˆopital’s rule to show that lim f(x) = 1...

(a) Consider the function f(x)=(ex −1)/x. Use l’Hˆopital’s rule to show that lim f(x) = 1 when x approaches 0 (b) Check this result empirically by writing a program to compute f(x) for x = 10−k, k = 1,...,15. Do your results agree with theoretical expectations? Explain why. (c) Perform the experiment in part b again, this time using the mathematically equivalent formulation, f(x)=(ex −1)/log(ex), evaluated as indicated, with no simplification. If this works any better, can you explain why?...

Consider the differential equation (x 2 + 1)y ′′ − 4xy′ + 6y = 0. (a)...

Consider the differential equation (x 2 + 1)y ′′ − 4xy′ + 6y = 0. (a) Determine all singular points and find a minimum value for the radius of convergence of a power series solution about x0 = 0. (b) Use a power series expansion y(x) = ∑∞ n=0 anx n about the ordinary point x0 = 0, to find a general solution to the above differential equation, showing all necessary steps including the following: (i) recurrence relation; (ii) determination...

Consider a Bernoulli random variable X such that P(X=1) = p. Calculate the following and show...

Consider a Bernoulli random variable X such that P(X=1) = p. Calculate the following and show steps of your work: a) E[X] b) E[X2] c) Var[X] d) E[(1 – X)10] e) E[(X – p)4] f) E[3x41-x] g) var[3x41-x]

Question