Define gluconeogenesis, glycogenolysis, and glycogenosis.

What conditions promote glycogenesis, glycogenolysis, and gluconeogenesis?

Solve the Bernoulli equations given in Problem. $(x+1)\left(y^{\prime}+y^{2}\right)=-y$

Define giycogenesis, glycogenolysis, and gluconeogenesis.

Evaluate the following expressions. Write in the form $f(x) + ig(x)$ for real-valued functions f, g. $\frac{d}{d x}\left(e^{2 i x} \cos (3 x)+\sin x\right)$

Define defecation reflex, constipation, and diarrhea.

Indicate whether the following enzymes is utilized in (1) glycogenesis but not glycogenolysis, (2) glycogenolysis but not glycogenesis, or (3) both glycogenesis and glycogenolysis: pyrophosphorylase

Why does it make metabolic sense for the same hormone signal to stimulate glycogenolysis and inhibit glycolysis in the liver while stimulating both glycogenolysis and glycolysis in muscles?

For points $\mathbf{u}$ and $\mathbf{v}$ in $\mathbb{R}^{n}$, define the function $p: \mathbb{R} \rightarrow \mathbb{R}$ by

$$p(t)=\|\mathbf{u}+t \mathbf{v}\|^{2}$$

for t in $\mathbb{R}$. Show that p(t) is a quadratic polynomial that attains only nonnegative values. Use this to show that the discriminant is nonpositive and thus provide another proof of the Cauchy-Schwarz Inequality.

When a small amount of iodine is added to a mixture of chlorine and methane, it prevents chlorination from occurring. Therefore, iodine is a free-radical inhibitor for this reaction. Calculate $\Delta H^{\circ}$ values for the possible reactions of iodine with species present in the chlorination of methane, and use these values to explain why iodine inhibits the reaction. (The I-CI bond-dissociation enthalpy is 211 kJ/mol or 50 kcal/mol.)

Show that the given set of functions forms a fundamental set of solutions to the differential equation on $(-\infty, \infty)$. $\{1, \cos x, \sin x\}, y^{\prime \prime \prime}+y^{\prime}=0$

A word family is a group of words that share the same origin or that were all formed from a common base word. For instance, the words purified and purification, which appear in "By the Waters of Babylon," are part of the same word family as the word pure. Identify two other words that belong to the same word family as purified, purification, and pure.

(i) sketch the differential equation in the $y-y^{\prime}$ plane by hand. (ii) Draw the phase line diagram, clearly stating the location and stability of the equilibria. (iii) State the long-term behavior for all initial conditions. (iv) Assuming y = y(x), sketch the corresponding graph in the traditional x-y plane. $y^{\prime}=-y^{2}$

Suppose that $\mathcal{V}=\left\{\mathbf{v}_{1}, \ldots, \mathbf{v}_{m}\right\}$ spans a vector space V, and suppose that v is in V but not in $\mathcal{V}$. Prove that $\left\{\mathbf{v}, \mathbf{v}_{1}, \dots, \mathbf{v}_{m}\right\}$ is linearly dependent.