Describe the technique for finding $\int \sec ^{5} x \tan ^{7} x dx$. Do not integrate.

What is the frequency of the photon emitted when the electron in a hydrogen atom drop s from the n = 3 Bohr orbit to the n = 2 Bohr orbit?

sketch a graph of the function and approximate the limit (if it exists). Then find the limit (if it exists) algebraically by using appropriate technique(s).

$$lim x→5 √x-2/x-5$$

Review the meaning of the vocabulary word listed below. Then, write a sentence in which you define the word .

confederation

Solve for the variable without using a calculator. (If necessary, review Section $2.6$).

$$y=\ln\sqrt{e}$$

Solve for the variable to two decimal places. (If necessary, review Section $2.5$).

$$10,0000 = 7,500e^{0.085t}$$

Simplify. If possible, use a second method or evaluation as a check.

$$\dfrac{\dfrac{x^2-x-12}{x^2-2 x-15}}{\dfrac{x^2+8 x+12}{x^2-5 x-14}}$$

$$\textbf{\textcolor{#4257b2}{Mixed Review}}$$

Evaluate.

$t^4 + 1$ for $t = 2$

Simplify. If possible, use a second method or evaluation as a check.

$$\dfrac{\dfrac{y^2}{y^2-9}-\dfrac{y}{y+3}}{\dfrac{y}{y^2-9}-\dfrac{1}{y-3}}$$

Use the technique of completing the square to evaluate the following integrals. $\int \frac { 1 } { x ^ { 2 } + 2 x + 1 } d x$

Which technique is useful in evaluating the integral?

$$\displaystyle \int \frac{x^{2}}{1-x^{2}}\ dx$$

(e) A trig substitution

For $f(x)=x^{2}-2 x$ on the interval [0, 2], list the evaluation points for the Midpoint Rule with n=4, sketch the function and approximating rectangles and evaluate the Riemann sum.

Use the technique of completing the square to evaluate the following integrals. $\int \frac { 1 } { x ^ { 2 } - 6 x } d x$

Sodium hydrogen carbonate (baking soda) easily decomposes to release sodium carbonate, water, and a gas. Cake batter rises because of the decomposition of sodium hydrogen carbonate.

(a) What gas is produced? [Hint: It turns limewater cloudy.]

(b) Write a balanced chemical equation for this reaction.