8.2, 8.3, 8.4, 9.1, 9.2, 9.3 Review Formulas / MATH16B

9.1 Functions of HYPERBOLOID

• To create a three-dimensional shape with a saddle point

• To represent a quadratic surface in three-dimensional space

• To model hyperbolic functions in calculus

• To generate a parabolic curve in two-dimensional space

8.3 TOTAL MONEY FLOW Formula IS what?

• Total Income - Total Expenses

• Total Assets - Total Liabilities

• Total Revenue + Total Costs

• Total Cash Inflows - Total Cash Outflows

9.1 Functions of PARABOLOID

• Reflecting light to a focal point

• Storing energy

• Creating sound waves

• Generating electricity

8.3 VOLUME OF REVOLUTION formula IS what?

• πr²h

• 2πrh

• (1/3)πr²h

• (1/2)πr²h

8.3 AREA BETWEEN CURVES Formula IS what?

• 1.) Set f(x), g(x) equal to find Intersection points

• 2.) Calculate the area using definite integrals

• 3.) Find the maximum value of the function

• 4.) Determine the slope of the curves at the intersection

9.2 Intro to Partial Derivatives

• Understanding the concept of derivatives in single-variable calculus

• Learning how to compute limits in multivariable calculus

• Exploring the definition and applications of partial derivatives

• Studying the fundamental theorem of calculus

8.4 IMPROPER INTEGRAL formula IS what? pt 2

• \int_{a}^{b} f(x) dx = \lim_{t \to b} \int_{a}^{t} f(x) dx

• \int_{a}^{\infty} f(x) dx = \lim_{t \to \infty} \int_{a}^{t} f(x) dx

• \int_{0}^{1} f(x) dx = \lim_{t \to 1} \int_{0}^{t} f(x) dx

• \int_{-\infty}^{\infty} f(x) dx = \lim_{t \to -\infty} \int_{t}^{\infty} f(x) dx

8.2 AVERAGE VALUE Formula IS what?

• (1) (1/b-a) ∫[a,b] f(x) dx

• (2) (b-a) / 2

• (3) (1/n) Σ f(x)

• (4) (b^2 - a^2) / 2

8.4 IMPROPER INTEGRAL formula IS what? pt 1

• \( \int_{a}^{\infty} f(x) \, dx \)

• \( \int_{0}^{1} f(x) \, dx \)

• \( \int_{-\infty}^{\infty} f(x) \, dx \)

• \( \int_{b}^{c} f(x) \, dx \)

9.1 Functions of ELLIPSOID

• To represent three-dimensional shapes

• To calculate the volume of a sphere

• To model the Earth's shape

• To define linear equations