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Show that the equation z 3 -1- 2e‘ = 0 has exactly one solution. State clearly every result you use and show that the conditions are satisfied. (Hint: Start by showing that there is at least one solution and then exclude the possibility of more solutions.)
Use the previous problem to show that sin(x) + x = 0 has exactly one solution in R. Hint: Show that it has at most one solution, then show it has at least one solution.
i want step by step
Show that the equation e-2x + 5 cos(13x) = 0 has a unique solution forxE0, 13
Show that the equation e-2x + 5 cos(13x) = 0 has a unique solution forxE0, 13
14. For A- a b show that if ad-be 0, then the equation Ax 0 has more than one solution. Why does this imply that A is not invertible? Hint: First, consider ab 0. Then, if a and b are not both zero, consider the ectorxI you use the word "determinant, then be sure to justify your statement thoroughly
23. Consider the Bessel equation of order zero (a) Show thatr 0 is a double root of the indicial equation. (b) Find one solution of the form 4 22 22.42 22.42.62 This solution is known as Jo(t). (c) Find a second solution using the method of reduction of order
23. Consider the Bessel equation of order zero (a) Show thatr 0 is a double root of the indicial equation. (b) Find one solution of the form 4 22 22.42 22.42.62...
Please show all work
Show that R_1, 0 is a solution of the radial wave equation.
Multiplicity: Please use Write the equation of a polynomial that has exactly 2 distinct real zeros: one that is positive and one that is negative. Also, the positive multiplicity (but not 1)(use 3 or even multiplicity (but not 0) (use 2 or higher). You decide on the leading integer coefficient, only integers for all constants required! zero is to have odd higher) whereas the negative zero will have a 1. Write the polynomial equation below using the form:
P3.* Consider the ordinary differential equation: u” + 1 = 0. a) Show that this equation together with the boundary conditions u(0) = 2, u(a) = 0 has no solution. b) Show that this equation together with the boundary conditions u(0) = 2, u(a) = –2 has infinitely many solutions.
0. (Bonus 2 points) Given the Eº for the following half-reactions: Cut + e → Cu° Eºred = 0.52 V Cu2+ + 2e → Cu° Eºred = 0.34 V What is Eº for the reaction: Cut → Cu2+ + e? Show your work. (Hint: It is not as simple as problem 2. You may want to start from the definition of standard voltage)
4. Differential equation. Show that if ψ(x) is a solution of the one-dimensional time-independent Schrödinger equation, then c ψ(x), where c is an arbitrary complex constant, is also a solution.