Does the assumption concerning the reinvestment of intermediate cash inflow tend to favor NPV or IRR? In practice, which technique is preferred and why?

In this exercise, find the indicated products directly by inspection. It should not be necessary to write down intermediate steps.

$$(3 v-2)(3 v+2)$$

Use the Intermediate Value Theorem to find the value of $c$ such that $f(c)=M$.

$$f(x)=\frac{x-1}{x+1} \text{ on } [-4,-2] ; \quad M=2$$

Use the intermediate-value theorem to show that the equation has a solution in the interval specified.
$x^3-3x-4=0, \quad [2,3]$.

Suppose that a function is continuous on [0, 1] except at 0.25 and that f(0)=1 and f(1)=3. Let N=2. Sketch two possible graphs of f, one showing that f might not satisfy the conclusion of the Intermediate Value Theorem and one showing that might still satisfy the conclusion of the Intermediate Value Theorem (even though it doesn’t satisfy the hypothesis).

Volume Use the Intermediate Value Theorem to show that for all spheres with radii in the interval $[1,5]$, there is one with a volume of $275$ cubic centimeters.

More than two decades elapsed between the development of a homogeneous catalytic process for producing acetic acid in the late 1960 s and convincing experimental evidence for the key intermediate $\left[\mathrm{CH}_3 \mathrm{Rh}(\mathrm{CO})_2 \mathrm{I}_3\right]^{-}$ (Figure 14.20). Describe the evidence presented for this intermediate.

Compare the intermediate benzenonium ions for ortho, meta and para bromination of benzoic acid, and explain why the main product is m-bromobenzoic acid.

Reaction of an alcohol with thionyl choride in the presence of a tertiary amine (c.g., pyridine) affords replacement of the OH group by Cl with inversion of configuration. However, if the amine is omitted, the result is usually replacement with retention of configuration. The same chlorosulfite intermediate is involved in both cases. Suggest a mechanism by which this intermediate can give the chloinated product without inversion.

Use the following terms to create a concept map: igneous rock, magma, coarse grained, fine grained, felsic, mafic, and intermediate.

In this exercise, find the indicated products directly by inspection. It should not be necessary to write down intermediate steps.

$$(2 x y-11)(2 x y+11)$$

Use induction to prove that radix sort works. Where does your proof need the assumption that the intermediate sort is stable?

In this exercise, find the indicated products directly by inspection. It should not be necessary to write down intermediate steps.

$$(4 x-5 y)(4 x+5 y)$$

There were 13 original states. There are now 50 states. What fraction of the states are the original states?