Given the following array definition:

int values[] = {2, 6, 10, 14};

What does the given statement display?

 cout << values[2];

Find and compare the values of $dy$ and $\Delta y$ for each function at the given values of x and $d x=\Delta x$. $y=x^{3}+x^{2}+3$ at $x=1$ and $d x=\Delta x=-0.05$

Given a=10 and $B=150^{\circ}$ in triangle ABC, determine the values of b for which A has (a) exactly one value, (b) two possible values, (c) no value.

Solve the following problems for x(t). Compare the values of x(0+) and x(0−). For parts (b) through (d), also compare the values of (0+) and (0−).a. b. c. d.

Explain for which values of a the function $a^{2}$ is increasing and for which values it is decreasing. Use the fact that, for a>0, $\frac{d}{d x}\left(a^{x}\right)=(\ln a) a^{x}$.

Find two $z$ values, one positive and one negative, that are equidistant from the mean so that the areas in the two tails add to the following values. \

$$5 \%$$

Find all the angle values of the trigonometric functions that have the given values. Give answers in degree measures rounded to the nearest tenth.

$$\sin x = 0.64$$

Find the values of x for which the given geometric series converges. Also, find the sum of the series (as a function of x) for those values of x.

$$\sum _ { n = 0 } ^ { \infty } 2 ^ { n } x ^ { n }$$

Find the values of A and B for which the equation $2 x + 3 = A ( x + 3 ) + B ( x - 1 )$ is an identity (true for all values of x. [Hint: Evaluate both sides at x = 1 and x = - 3]

If z = 0.60x + 0.95y for the set of values of (x, y) represented by the polygonal region bounded by graphs of $x=40, y= 30, 2y+x=280$ and $x-y=100$. what are the maximum and minimum values of z?

Compare $f(x)=x^{2}$ and $g(x)=2^{x}$ for x=1/2, x=1, x=2, x=3 and x=4. In general, which function is bigger for large values of x? For small values of x?

Given the following array definition:

int values[] = {2, 6, 10, 14};

What does the given statement display?

cout << values[1]++;

Find the absolute maximum and minimum values of $f ( x ) = \frac { x + 3 } { x - 3 }$, if any, in the interval $\lfloor - 5,5 \rfloor$, and state where those values occur.

Find and compare the values of $dy$ and $\Delta y$ for each function at the given values of x and $d x=\Delta x$. $y=\frac{x+5}{x+1}$ at $x=3$ and $d x=\Delta x=0.4$