Recursion relations to obtain the following recursion relations for spherical Bessel functions. We have written them for $j_n$, but they are valid for $y_n$ and for the $h_n’s.$ $(d / d x) j_{n}(x)=j_{n-1}(x)-(n+1) j_{n}(x) / x$

Your school has handed out a survey to students in order find out their opinions on different topics related to school life. Write two opinions for each category below, using complete sentences. The first one has been done for you. las horas de la escuela _____

Find each limit. Note that L'Hopital's rule does not apply to every problem, and some problems will require more than one application of L'Hopital's rule. $\lim _{x \rightarrow \infty} \frac{x^{2}}{e^{2 x}}$

A company reported average total assets of $1,240,000 in 2016 and$1,510,000 in 2017. Its net operating cash flow was $102,920 in 2016 and$138,920 in 2017. Calculate its cash flow on total assets ratio for both years. Comment on the results and any change in performance.

Read the sentences that tell what the people below used to do when they were your age. Then, answer the questions that follow in complete sentences. Follow the model. Modelo: Cuando Juliana y María tenían 14 años, ellas contaban muchos chistes (jokes). Se reían mucho y les gustaba ver las comedias en el cine. ¿Cómo eran las chicas? Ellas eran cómicas. ¿Adónde iban para ver las comedias? Iban al cine. ¿Y tú? ¿Qué hacías cuando eras niño(a)? ¿Cómo eras? ¿Adónde ibas? ¿Qué veías allí?

A 0.250-kg block resting on a frictionless, horizontal surface is attached to a spring whose force constant is 83.8 N/m. A horizontal force $\overrightarrow{\mathrm{F}}$ causes the spring to stretch a distance of 5.46 cm from its equilibrium position. (a) Find the magnitude of $\overrightarrow{\mathbf{F}}$. (b) What is the total energy stored in the system when the spring is stretched? (c) Find the magnitude of the acceleration of the block just after the applied force is removed. (d) Find the speed of the block when it first reaches the equilibrium position. (e) If the surface is not frictionless but the block still reaches the equilibrium position, would your answer to part (d) be larger or smaller? (f) What other information would you need to know to find the actual answer to part (d) in this case? (g) What is the largest value of the coefficient of friction that would allow the block to reach the equilibrium position?

Find the consumers' surplus and the producers' surplus at the equilibrium price level for the given pricedemand and price-supply equations. Include a graph that identifies the consumers'surplus and the producers' surplus. Round all values to the nearest integer. $p=D(x)=80-0.04 x ; p=S(x)=30 e^{0.001 x}$.

What amount of income tax is withheld from the salary of an employee who is single with two withholding allowances and earns $725 per week? What if the employee earns$625 and has no withholding allowances?

Your business associate mentions that she is considering investing in corporate bonds currently selling at a premium. She says that since the bonds are selling at a premium, they are highly valued and her investment will yield more than the going rate of return for the risk involved. Reply with a memorandum to confirm or correct your associate’s interpretation of premium bonds.

You just finished watching the evening news. Under each news category below, write a short summary of the stories of the day by looking at each picture and using appropriate vocabulary. The first one has been started for you. El tiempo Hoy pasó un gran huracán por las islas de Venezuela. _____

Which of the following equations have the same solution? Give reasons for your answer that do not depend on solving the equations. a. x+3=5x-4. b. x-3=5x+4. c. 2x+8=5x-3. d. 10x+6=2x-8. e. 10x-8=2x+6. f. $0.3+\frac{x}{10}=\frac{1}{2} x-0.4$.

Apply the Pauli exclusion principle to determine the number of electrons that could occupy the quantum states described by $n=3, \ell=1$.

Why is the following situation impossible? An ideal gas undergoes a process with the following parameters: Q = 10.0 J, W = 12.0 J, and $\Delta T=-2.00^{\circ} \mathrm{C}$.

Simplify each expression. Assume all variables represent positive real numbers. $-\sqrt[3]{\frac{5}{8}}$