Express the limit as an integral (or multiple of an integral) and evaluate.

$$\lim _ { N \rightarrow \infty } \frac { 5 } { N } \sum _ { j = 1 } ^ { N } \sqrt { 4 + 5 j / N }$$

Demandez $\`{a}$ votre partenaire de décrire un voyage (réel ou imaginaire). Vous pouvez utiliser les suggestions suivantes.

• o$\`{u}$ / aller?

• comment / voyager?

• quand / partir?

• combien de temps / rester l$\`{a}$-bas?

• quels endroits / visiter?

• qu’est-ce que / faire?

• qui / rencontrer?

• de qui / faire la connaissance?

• o$\`{u}$ / sortir?

• quand / rentrer?

Express each limit as an integral $\lim _{n \rightarrow \infty} \frac{f(1 / n)+f(2 / n)+\cdots+f(n / n)}{n}$

Express each limit as an integral $\lim _{n \rightarrow \infty}\left(\frac{n+1}{n^{2}}+\frac{n+2}{n^{2}}+\cdots+\frac{2 n}{n^{2}}\right)$

Find the limit (if it exists). If the limit does not exist, explain why. Use a graphing utility to verify your result graphically. $\lim _{x \rightarrow-\infty}\left[\frac{6 x^{2}}{(x+1)^{2}}-4\right]$

Sketch and identify the surface. $9 x^{2}+y^{2}+z=9$

Find the indicated limits. $\lim _{t \rightarrow 1} \frac{\ln (\ln t)}{\ln t}$

Solve. Identify all double roots.

$$x ^ { 2 } \left( x ^ { 4 } + 16 \right) = 8 x ^ { 4 }$$

Uranium-238 $(U^{238} )$ has three more neutrons than uranium-235 $(U^{235} )$ . Compared to the speed of sound in a bar of $U^{235}$ , is the speed of sound in a bar of $U^{238}$ higher, lower, or the same? Explain your choice, including justification for assumptions you make.

There is a famous photo taken of the famous participants in the Fifth Solvay Congress. Identify at least 10 participants and discuss what their contributions were to quantum physics.

You found that a function formula for an arithmetic sequence with initial term $t_{0}$ and common difference is

$$t_{n }=t_{0}+d n$$

. Using the form $t_{n}=\ldots,"$ write a similar function formula if the initial term is $t_{1}$, instead of $t_{0}$.

What does ATP stand for? What is the role of ATP in living organisms?

(a) What three fears does Juliet reveal in her Act IV, Scene iii, soliloquy? (b) What does the soliloquy reveal about her personality? Explain your response and support it with references to the text.

Based on the pictures, write the activity that the first person likes or does not like to do. Then, complete the second person´s response.

Jaime: No me gusta... ¿A ti te gusta? Julio: No,...