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Verified Documents at University of California - Davis

Calculus
University of California - Davis
Verified Notes

Browse the full collection of course materials, past exams, study guides and class notes for MAT 21A - Calculus at University of California - Davis verified by our community.

PROFESSORS

All Professors

Janko Gravner

Michael Kapovich

Andrew Waldron

Korana Burke

Eric Babson

Andre Kornell

Anne Schilling

Verified Documents for Anne Schilling

Class Notes

Taken by our most diligent verified note takers in class covering the entire semester.

MAT 21A Lecture 4: Solving Limits and Percise Definition Introduction

Lets use quotient ruler as long as denominator. Lim f t limxe lim i t him 7 t xx. The sumdif duke gives us theirtheorem if pub anxhtan ex t al_thentimp

MAT 21A Lecture 5: Definition Of Limit And How To Solve For Delta And Epsilion

Weneed todo r 0 lix 11 8 beatboth. Basically you observea function on a openinterval around xo which is a point youchoose. lyyen. Xo1 c our limitis goi

MAT 21A Lecture 6: Winter 2019 Limits Continuinity Sandwich Theorem

Onesided limits t fats f y x o. If all of e are greaterthan o thereexist. 870 so thereforetheres him flex l the inequality x rotor whichessentially is

MAT 21A Lecture 8: Continuity examples(REAL Lecture 8)

Alotofoperationsyoucandowith realft"syou can dowithfunctions aswell exs pdyxp. ci 5anxntanixn t. Lecture 8 a x ta is continuous since life pen pcc ex r

MAT 21A Lecture 9: Continuity Of Inverse And Composite Functions And IMVT

Anotherday of continuity this time we"re reviewing inverse continuity a functionis continuous and its definedwithin an tsimply interval then its invers

MAT 21A Lecture 10: Horizontal, Vertical, Slant Asymptotes, End Behavior Model

MAT 21A Lecture 11: The Derivative Function

1 means that insteadof finding the derivative of. This might be tedious but our professor really wanted to hit a homerun with this ideaxoisnowsimpl. lt

MAT 21A Lecture Notes - Lecture 12: Product Rule

MAT 21A Lecture 13: Product, Quotient, Negative Power, and Higher Power Derivatives

MAT 21A Lecture 14: Average Rate Of Change, Motion, Velocity, and More

Instantaneous rate ofa f xt h h flex. F xo lim flxoth h o h f xo. Thus instantaneous rates are limits of average rates providedthe limit exist cha. So

MAT 21A Lecture 15: Trig Derivatives and Velocity, Acceleration Example

MAT 21A Lecture Notes - Lecture 16: Mondego River

MAT 21A Lecture 17: Implicit Differentiation

MAT 21A Lecture Notes - Lecture 18: Cud

MAT 21A Lecture 20: Inverse Trig. Derivatives and Related Rates Intro

Ln 17 18 a quick review on trig derivatives. This is since cos cos c sincx an ex j cot cx. Cos sinct when finding the inverse of it a trig function is

MAT 21A Lecture 21: Another Related Rates Example

In this section we look questions that arise when two or more related quantities are changing to solve follow the. Is the problem name variables and ar

MAT 21A Lecture 22: Linearization

MAT 21A Lecture 23: Differentials and Examples

Not change in x flit dx change in f approximate change in f the same but dare ftho. Remember that this does not mean its ratio d_y dx. Introducing new

MAT 21A Lecture Notes - Lecture 24: If And Only If

Exampies a find all criticalpoints off find all points f hasglobal max c find all points f has globalmin. Hx 4 x on c1,33 fix x3 3 on c2,2 fix x 45 on

MAT 21A Lecture Notes - Lecture 25: Mean Value Theorem, Twill, Qoph

Before introducing the mean ohne theron we must. Suppose fca is a function that satisfies all of the i y 9 continuous on the closedintervalea b. Acc b

MAT 21A Lecture Notes - Lecture 26: Telomerase Reverse Transcriptase, Cascading Style Sheets

MAT 21A Lecture Notes - Lecture 27: Qoph, Inflection

Recall thatthe 1st derivative tells us if thefunction in increasing or decreasingthe secondderivative gives us information about howtheqoph of the diff

MAT 21A Lecture Notes - Lecture 28: Ney

If f is definedaxon ca if him f l at. I odflinggfaf. h doesnotexist and is too thenthereis an asymptote o: dffindefinedan iq co then if fights r thenth