Get started today!

Good to have you back!
If you've signed in to StudyBlue with Facebook in the past, please do that again.

- StudyBlue
- Wisconsin
- University of Wisconsin - Madison
- Mathematics
- Mathematics 221
- Kiselev
- mid221109material.pdf

Jas M.

Deflnitions, statements and proofs that may appear on the flrst midterm Math 221 The material for the flrst midterm includes prerequisites, everything we covered about limits, everything we covered about continuity, and the Tuesday September 22 lecture’s material on derivatives (basically, just the deflnition, using this deflnition to compute derivatives of simple functions, and tangent lines). Most problems on the test will be computational. In addition to more compu- tational problems, a few questions on the test may ask you to state a deflnition or theorem, or to prove some property. The list of the deflnitions and properties that may be on the test appears below. Not all these questions will appear on the test, of course. Deflnitions and statements: 1. Deflne what does it mean that the function f(x) is continuous at x = a: 2. Deflne the derivative of a function f(x) at x = a: 3. State the limit laws for addition, subtraction, multiplication and division. 4. State Sandwich Theorem. 5. State Intermediate Value Theorem for continuous functions. 6. Write the equation of a tangent line to the graph y = f(x) of a difierentiable function f at a point (a;f(a)): Proofs: 1. †¡– proof that the limit exists and is equal to something for simple functions. 2. Prove that if f(x) is difierentiable at x = a; then it is continuous at x = a: You may use without proof the limit laws (for the limits of sum, difierence, product and quotient), but you should state which property are you using in each step. 1

Advertisement

Advertisement

"StudyBlue is great for studying. I love the study guides, flashcards and quizzes. So extremely helpful for all of my classes!"

Alice , Arizona State University"I'm a student using StudyBlue, and I can 100% say that it helps me so much. Study materials for almost every subject in school are available in StudyBlue. It is so helpful for my education!"

Tim , University of Florida"StudyBlue provides way more features than other studying apps, and thus allows me to learn very quickly!??I actually feel much more comfortable taking my exams after I study with this app. It's amazing!"

Jennifer , Rutgers University"I love flashcards but carrying around physical flashcards is cumbersome and simply outdated. StudyBlue is exactly what I was looking for!"

Justin , LSU