Exam 2 Review

Exam 2 will take place on Wednesday, July 9 during the first half of class, 10:30-11:30 am (the second portion of class will be lecture). You will need a scientific calculator. You may use a graphing calculator. However, calculators with computer algebra systems (TI-89, TI-nSpire CAS, etc.), iPads, cell phones, and other technologies will not be allowed on the exam. You will be provided with a formula sheet and scratch paper. No other resources will be permitted on the exam.

Terminology: Traces Functions of several variables Level curves (contour maps) and Level Surfaces Continuous function of several variables Domain/Range of a multivariable function Partial Derivatives Clairaut’s Theorem Tangent Plane Linearization (tangent plane approximation) Differentials (total differential) Directional Derivatives Gradient vector Normal line Local maximum, local minimum, absolute maximum, absolute minimum Critical point Saddle point Bounded set Closed set Lagrange multiplier Constraint

Concepts and Skills: Prerequisite skills: limits (including basic indeterminate forms/L’Hospital’s Rule),

differentiation (product rule, chain rule), integration (u-substitution), dot product, cross product, equations of lines, equations of planes, basic graphs of conic sections (parabolas, ellipses, hyperbolas)

Determine the domain and range of multivariable functions Sketch the domain of a multivariable function Sketch a multivariable function Determine if multivariable functions are continuous Compute partial derivatives Determine if a function is a solution to a partial differential equation Use the total differential to estimate quantities Use the chain rule Implicit differentiation Compute directional derivatives Find the maximum rate of change of a function and the direction in which it occurs Compute the equation of a tangent plane Compute the equation of a normal line

Find critical points for functions of two variables Classify local extrema of a function Optimization with constraints (Lagrange’s Method)

Given Formulas: Linearization of f at (a,b) Total Differential Second Derivatives Test

Need to know from memory: Basic trigonometry (evaluating trig functions of special angles, Pythagorean

identities) Basic calculus skills (See concepts/skills) Chain Rule Equation of tangent plane Equation of normal line Directional Derivative Gradient Method of Lagrange Multipliers

Study Tips: The best way to learn math is by doing math! If you study by reading through your

notes and examples, that will likely not be sufficient. Be sure to practice problems. You may want to practice problems using the formula sheet you are given on the exam (see D2L-content-formula sheets for a copy of the formula sheet).

Looking for problems to practice? I am not suggesting that you need to work all of the problems listed below, but you should work enough problems that you feel comfortable with topics from each section. There are many resources available to you:

o WebAssign review problems-You will find these posted in WebAssign. They do not count toward your homework score, but you may find it helpful to practice these problems.

o Rework past homework problems-You can view the key on past due assignments in WebAssign to check your work.

o Rework examples down in class.o Rework written homework problems and in-class activity problems

(solutions can be found in D2L)o Rework examples in the textbook. The ebook has many video examples to

accompany textbook examples online. o Practice odd problems from the book. The student solution manual is

available at the library for check out. Use the list of terminology and concepts/skills to help you know which topics to

study. Questions… email me, or stop by office hours.