For each function f, find the limit as x approaches c of the average rate of change of f from c to x. That is, find $\lim _{x \rightarrow c} \frac{f(x)-f(c)}{x-c}$. $f(x)=\sqrt{2 x}, c=5$

The Fibonacci sequence is defined recursively as follows: $f_0=0, f_1=1, f_{f}=f_{(f−1)}+f_{(f−2)}$ for all integers $f$ with $f\ge 2$. The first few terms are $0, 1, 1, 2, 3, 5, 8, 13$. Prove that

$$f_f= \frac{1}{\sqrt{5}}\left(\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}\right)$$

for every non-negative integer $f$.

determine the general solution of the given differential equation that is valid in any interval not including the singular point. x2y''+2xy'+4y=0

Échanges: Les magasins d'alimentation

Regardez les dessins ci-dessus et posez des questions $\`{a}$ votre camarade de classe.

MOD$\`{E}$LE: É1: O$\`{u}$ est-ce qu'on peut trouver des pommes?

É2: Chez le marchand de fruits et légumes.

$`{E}$1: Tu aimes les pommes?

E2: Oui, j'aime $\`c{c}$a. J'en mange beaucoup.

(Non, pas tellement. Je préf$\`{e}$re les bananes.)

É2: O$\`{u}$ est-ce qu'on vend des homards?

É1: Tu vas $\`{a}$ la poissonnerie.

É2: Tu aimes $\`c{c}$a, toi?

É1: Oui, j'adore le homard. Mais $\`c{c}$a coute tr$\`{e}$s cher!

(Ah non, pas du tout! Je n'aime pas le gout.)

Solve for c, where c represents the length of the hypotenuse of a right triangle. Simplify the result, if possible. a.

$$c ^ { 2 } = 64$$

b.

$$c ^ { 2 } = 15$$

c.

$$c ^ { 2 } = 24$$

Find each exact function value. $\cot \frac{5 \pi}{6}$

Is InchesInOneCentimeter a valid C++ identifiers?

The following table gives the distribution of the life time of 400 neon lamps :

$$\begin{array}{|c|c|} \hline Life time (in hours) & Number of lamps \\ \hline 1500-2000 & 14 \\ 2000-2500 & 56 \\ 2500-3000 & 60 \\ 3000-3500 & 86 \\ 3500-4000 & 74 \\ 4000-4500 & 62 \\ 4500-5000 & 48 \\ \hline \end{array}$$

Find the median life time of a lamp.

Determine whether each of the following molecules is polar or non-polar: $\mathrm{KNO}$

(a) $\mathrm{CCl}_4$

(b) $\mathrm{H}_2 \mathrm{O}$

(c) $\mathrm{HF}$

(d) $\mathrm{CF}_4$

(e) $\mathrm{CH}_3 \mathrm{Cl}$

a. The volume, V, of a cylinder is given by the formula V = $\pi r^2L$ where r is the cylinder’s radius and L is its length. Using this formula, write a C++ function named cylvol() that accepts a cylinder’s radius and length and returns its volume. b. Include the function written in previous Exercise in a working program. Make sure your function is called from main() and returns a value to main() correctly. Have main() use a cout statement to display the returned value. Test the function by passing various data to it.

Solve each equation. Check your solutions.

2|b + 4| = 48

Expand $f(z)=\frac{1}{z(z-3)}$ in a Laurent series valid for the indicated annular domain. 1<|z-4|<4

Compare and Contrast How are plateaus and mountains alike? How are they different?

Find the cardinal number of given of the following sets. Assume the pattern of elements continues in given part in the order given.
a.{201, 202, 203, ...... ,1100}
b.{1, 3, 5, ..... , 101}
c.{1, 2, 4, 8, 16, ..... , 1024}
d. {x|x = $k^{3}$ , k = 1, 2, 3, ..... ,100}