Find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = tan x, a = π

Fill in the blank with an appropriate word, phrase, or symbol(s). For any event A, P(A)+P(not A)=_.

What is meant by a chemical bond? Why do atoms form bonds with each other? Why do some elements exist as molecules in nature instead of as free atoms?

Find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = x + 1/x, a = 1

Factor the polynomial.

$$x ^ { 2 } - 400$$

Find the linearization L(x) of f(x) at x = a. f(x) = x^3 - 2x + 3, a = 2

Solve the equation. Check for extraneous solutions.

$$\log _ { 5 } ( x + 4 ) + \log _ { 5 } ( x + 1 ) = 2$$

A rigid motion $F:R^2\to R^2$ is given. Use the given information to find the orthogonal matrix $Q$ and the vector $b$ such that $F(v)=Qv+b$ for all $v$ in $R^2$.

$$\begin{equation*} F\begin{pmatrix}\begin{bmatrix}2\\1\end{bmatrix}\end{pmatrix}=\begin{bmatrix}1\\2\end{bmatrix}, F\begin{pmatrix}\begin{bmatrix}1\\3\end{bmatrix}\end{pmatrix}=\begin{bmatrix}2\\0\end{bmatrix}\text{ and } F\begin{pmatrix}\begin{bmatrix}7\\1\end{bmatrix}\end{pmatrix}=\begin{bmatrix}4\\6\end{bmatrix} \end{equation*}$$

A gaseous mixture of 0.5 lbmol of methane and 0.5 lbmol of propane occupies a volume of $7.65 ft^3$ at a temperature of $194^\circ F.$ Estimate the pressure using the following procedures and compare each estimate with the measured value of pressure, 50 atm a. the ideal gas equation of state. b. Kay's rule together with the generalized compressibility chart. c. the van der Waals equation together with mixture values for the constants a and b. d. the rule of additive pressure together with the van der Waals equation. e. the rule of additive pressure together with the generalized compressibility chart. f. the rule of additive volume together with the van der Waals equation.

Use integration tables to find the indefinite integral. ∫ cos θ / (3 + 2 sin θ + sin² θ) dθ

Calculate the integral.

$$\int _ { - 1 / 2 } ^ { 0 } \frac { ( x + 1 ) d x } { \sqrt { 1 - x ^ { 2 } } }$$

What are the approximate chemical compositions of gasoline, diesel fuel, and natural gas?

Complete statement by writing the correct word or words. The general formula of a(n) ______ is ROH.

Suppose that

$$g _ { 1 } , g _ { 2 } , g _ { 3 } , \dots$$

is a sequence defined as follows:

$$g _ { 1 } = 3 , g _ { 2 } = 5$$

,

$$g _ { k } = 3 g _ { k - 1 } - 2 g _ { k - 2 }$$

for all integers

$$k \geq 3$$

. Prove that

$$g_n=2^n+1$$

for all integers

$$n \geq 1$$

.