Once an exothermic reaction begins, the reaction tends to keep going. Why?

What is the defining characteristic for an enzyme catalyzing a sequential reaction? A doubledisplacement reaction?

How does the antigen in an agglutination reaction differ from that in a precipitation reaction?

Let $(A, \mathscr{R})$ be a poset in which the length of a longest (maximal) chain is $n \geq 2.$ Let M be the set of all maximal elements in $(A, \mathscr{R}),$ and let B = A – M. If $\mathscr{R} = (B \times B) \cap \mathscr{R},$ prove that the length of a longest chain in $(B, \mathscr{R}),$ is n – 1.

Chain Rule This exercise proves the Chain Rule without the special assumption made in the text. For any number b, define a new function

$$F(u)=\frac{f(u)-f(b)}{u-b} \quad \text { for all } u \neq b$$

Observe that F(u) is equal to the slope of the secant line through (b, f(b)) and (u, f(u)).

Show that if we define $F(b)=f^{\prime}(b)$, then F(u) is continuous at u=b.

Draw a food chain diagram for an ecological area of interest to you (for example, a swamp, a field, a pond, or a tropical region). Model this food chain with a matrix $M$ and calculate $M^2 . M^3$, and $M+M^2+M^3$. Write a paragraph interpreting what the matrix $M+M^2+M^3$ tells you.

What is the difference between a single exchange reaction and a double exchange reaction?

At what protein complex location(s) in the electron transport chain does proton pumping occur?

Use the Chain Rule to find $dz/dt$ for $z=\cos(x+4y)$, $x=5t^4$, $y=1/t$.

Use Version 2 of the Chain Rule to calculate the derivatives of the following composite functions.

y = tan $e^x$

Once started, a(n) _ reaction tends to keep going.

Describe the changes in oxidation number that happen in an anode reaction and in a cathode reaction.

Explain the difference between a single replacement reaction and a double replacement reaction.

Separate this redox reaction into its balanced component half-reactions. Cl2+2Cu --> 2CuCl Oxidation half-reaction: Reduction half-reaction: