Carry out the following steps for the given functions f and points a. Find the linear approximation L to the function f at the point a.

$$f ( x ) = e ^ { - x }$$

, a=ln 2

An environmental study suggests that $t$ years from now, the average level of carbon monoxide in the air will be

$$Q(t)=0.05 t^{2} + 0.1 t+3.4$$

parts per million (ppm). By approximately how much will the carbon monoxide level change during the next 6 months?

$$2 \frac { 2 } { 3 } \div 1 \frac { 1 } { 2 }$$

Determine whether the sequence is increasing, decreasing or neither. $a_{n}=\frac{n-1}{n+1}$

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

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

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,...