Use a graph of f’’ to give better estimates.

$$f(x)=cosx+1/2cos2x, 0≤x≤2π$$

If possible, evaluate the quantities in the following exercise. Check your answer with a calculator.

$$(-32)^{3 / 5}$$

In a survey of 100 investors in the stock market, 50 owned shares in IBM 40 owned shares in AT&T 45 owned shares in GE 20 owned shares in both IBM and GE 15 owned shares in both AT&T and GE 20 owned shares in both IBM and AT&T 5 owned shares in all three

How many owned just IBM shares?

Suppose that $\int_{0}^{4} f(x) d x=5 \text { and } \int_{0}^{2} f(x) d x=-3$ and $\int_{0}^{4} g(x) d x=-1$ and $\int_{0}^{2} g(x) d x=2.$ in the following exercise, compute the integrals. $\int_{0}^{2}(3 f(x)-4 g(x)) d x$

Find the indicated quantities for the appropriate sequences.

$$d =\frac{4}{3},a_1=-3, a_n=17, n = ?$$

What stereochemistry would you expect for the product of the Diels–Alder reaction between (2E,4E)-2,4-hexadiene and ethylene? What stereochemistry would you expect if (2E,4Z)-2,4-hexadiene were used instead?

Match the inequality with its graph. [The graphs are labeled (a)–(h).]

$$x<3$$

On the line in each of the following sentences, rewrite the prefix and word in parentheses as a single word.

(over + cooking) Aunt Manuel was upset about $\underline{\hspace{2cm}}$ the stew.

What did you think would happen next?

Add commas where they are needed in the following sentences.

Example 1. My first grade teacher , Mrs. Dore , wrote me a letter last week.

12. Graham Greene the British novelist wrote screenplays for several films.

Consider

$$A=\left[\begin{array}{ll}0 & 1 \\ 0 & 3 \\ 5 & 6\end{array}\right], B=\left[\begin{array}{rr}-1 & 0 \\ 3 & 5 \\ 2 & 6\end{array}\right]$$

,

$$C=\left[\begin{array}{rr}-4 & 0 \\ 3 & 2\end{array}\right]$$

, and

$$D=\left[\begin{array}{rr}5 & 0 \\ -2 & 1\end{array}\right]$$

Calculate the following (if they exist).

(a) $2 A-3(B C)$ (b) $A B$ (c) $A C-B D$

(d) $C D-2 D$ (e) $B A$ (f) $A D+2(D C)$

(g) $C^3+2\left(D^2\right)\left(\right.$ where $\left.C^3=C C C\right)$.

Sketch the graphs of $y=x^n$ and the transformation. $y=x^4, \quad f(x)=2(x-2)^4$

Arrange the quantities from smallest to largest. 2.67 kl, 3000 ml, 14630 cl

Find each of the following quantities.

$$a) log_2 1024 b) log_2 1/4 c) log_4 8$$