# All Educational Materials for MAT135H1 at University of Toronto St. George (UTSG)

- About UTSG

## MAT135H1 Study Guide - Fall 2018, Comprehensive Term Test Notes - Confidence Trick, Francis Su, Calculator

0

## MAT135H1 Study Guide - Fall 2018, Comprehensive Term Test Notes - Graph Of A Function, Trigonometric Functions, Derivative

0

An assignment that assigns a real number, and another real number, f ( ) Therefore, we input a real number as and the result is the output which is ano

View Document## MAT135H1 Study Guide - Fall 2018, Comprehensive Quiz Notes - Trigonometric Functions, Graph Of A Function, Derivative

0

An assignment that assigns a real number, and another real number, f ( ) Therefore, we input a real number as and the result is the output which is ano

View Document## Trending

Frequently-seen exam questions from 2014 - 2018.

## MAT135H1 Lecture Notes - Lecture 34: Minimax, Maxima And Minima

0

Mat135 - lecture 34 - identifying local extrema. However, if f "( c ) = 0 and f ( c ) = 0 then we know need to assume the following case: C could be a

View Document## MAT135H1 Lecture Notes - Lecture 29: Maxima And Minima, Minimax, Cubic Function

0

Mat135 - lecture 29 - maximum and minimum values. We will begin to address it in this lecture and finish it next class. Given a function f on a domain

View Document## MAT135H1 Study Guide - Fall 2018, Comprehensive Term Test Notes - Graph Of A Function, Trigonometric Functions, Derivative

0

An assignment that assigns a real number, and another real number, f ( ) Therefore, we input a real number as and the result is the output which is ano

View Document## MAT135H1 Study Guide - Fall 2018, Comprehensive Quiz Notes - Trigonometric Functions, Graph Of A Function, Derivative

0

## MAT135H1 Lecture Notes - Lecture 25: Implicit Function, Searchlight, Pythagorean Theorem

0

Mat135 - lecture 25 - related rates part two. Read sections 3. 8 and 3. 9 from the textbook. The main steps to most related rates problems: Differentia

View Document## MAT135H1 Lecture Notes - Lecture 20: Implicit Function

0

Mat135 - lecture 20 - derivatives of logarithmic functions. Read sections 3. 6 and 3. 7 from the textbook. Recall that d dx e = e . Using implicit diff

View Document## MAT135H1 Lecture Notes - Lecture 22: Marginal Cost

0

Mat135 - lecture 22 - rates of change. Read sections 3. 6 and 3. 7 from the textbook. Recall the idea of interpreting derivatives as rates of change. L

View Document## MAT135H1 Lecture Notes - Lecture 19: Minute And Second Of Arc, Inverse Trigonometric Functions

0

Mat135 - lecture 19 - inverse trigonometric functions. Read sections 3. 5 and 1. 5 from the textbook. Recall that a function f has an inverse if and on

View Document## MAT135H1 Lecture Notes - Lecture 21: Logarithmic Differentiation

0

Mat135 - lecture 20 - derivatives of logarithmic functions. Read sections 3. 6 and 3. 7 from the textbook. As you can see, it is very messy. You need l

View Document## MAT135H1 Lecture Notes - Lecture 18: Implicit Function, Unit Circle

0

Read sections 3. 5 and 1. 5 from the textbook. So far, we"ve considered tangent lines of graphs and curves of a particular form: In the above, is expli

View Document## MAT135H1 Lecture 17: MAT135 - Lecture 17 - Chain Rule Part Three

0

Mat135 - lecture 17 - chain rule part three. Suppose g is differentiable at and f is differentiable at g ( ). In leibniz notation, if = f ( u ) is diff

View Document## MAT135H1 Lecture 16: MAT135 - Lecture 16 - Chain Rule Part Two

0

Mat135 - lecture 16 - chain rule part two. Suppose g is differentiable at and f is differentiable at g ( ). In leibniz notation, if = f ( u ) is differ

View Document## MAT135H1 Lecture Notes - Lecture 12: Quotient Rule, Product Rule

0

Mat135 - lecture 12 - product and quotient rules. Read sections 3. 1 -3. 3 from the textbook. If f and g are differentiable at then d dx ( f ( ) G ( ))

View Document## MAT135H1 Lecture Notes - Lecture 13: Quotient Rule, List Of Trigonometric Identities

0

Mat135 - lecture 13 - derivatives of trigonometric functions. Read sections 3. 1 -3. 3 from the textbook. 0 sin / = 1 ( cos - 1 / ) = 0. Calculate lim

View Document## MAT135H1 Lecture 14: MAT135 - Lecture 14 - Chain Rule

0

Read sections 3. 4, 3. 5, and 1. 5 from the textbook. Suppose g is differentiable at and f is differentiable at g ( ). In leibniz notation, if = f ( u

View Document## MAT135H1 Lecture Notes - Lecture 10: Difference Quotient

0

Mat135 - lecture 10 - the derivative as a function. Read sections 2. 7 -2. 8 from the textbook. F "() = lim h 0 f (+ h ) - f () / h. If f "() exists, w

View Document## MAT135H1 Lecture Notes - Lecture 9: Difference Quotient

0

Mat135 - lecture 9 - derivatives and rates of change. Read sections 2. 7 -2. 8 from the textbook. For = f (), the slope of the tangent line at ( a , f

View Document## MAT135H1 Lecture Notes - Lecture 8: Asymptote, Coefficient

0

Read sections 2. 5 -2. 6 from the textbook. Instead of considering the limits where f ( ) limits where (end behaviour of f ( )) , we now focus on looki

View Document## MAT135H1 Lecture Notes - Lecture 7: Intermediate Value Theorem, Trigonometric Functions, Asymptote

0

Mat135 - lecture 7 - infinite limits and continuity. Read sections 2. 5 -2. 6 from the textbook. If f ( ) > 0 near (but not equal to) a , f ( ) grows a

View Document## MAT135H1 Lecture 6: MAT135 - Lecture 6 - Calculating Limits using Limit Laws

0

Mat135 - lecture 6 - calculating limits using limit laws. Assume lim x a lim x a f ( ) , c = c lim x a g ( ) exist. 1 be a positive integer and c . G (

View Document## MAT135H1 Lecture Notes - Fall 2018 Lecture 4 - The Tangent, The Tangent, Drag (physics)

0

Mat135 - lecture 4 - the tangent and velocity. Read sections 2. 1 -2. 3 from the textbook. The objective is finding the v (instantaneous) Assume that t

View Document## MAT135H1 Lecture Notes - Fall 2018 Lecture 5 - Ç€Xam language, Ç€Xam language

0

Mat135 - lecture 5 - the limit of a function. Q: using the above graph of f , find the following limits, if they exist lim x 1 lim x 2 lim x 4 lim x 5

View Document## MAT135H1 Lecture Notes - Lecture 3: Pythagorean Theorem

0

Read sections 1. 1 -1. 5, appendix d from the textbook. Let ( , ) be a point on the circle of radius r associated with angle . All angles will be in ra

View Document## MAT135H1 Lecture Notes - Lecture 2: Quotient Rule, Power Rule, Product Rule

0

Mat135 - lecture 2 - exponentials and logarithms. Read sections 1. 1 -1. 5, appendix d from the textbook. Exponential functions follow the form f ( ) =

View Document## MAT135H1 Lecture Notes - Lecture 1: Inverse Function

0

Read sections 1. 1 -1. 5, appendix d from the textbook. An assignment that assigns a real number, and another real number, f ( ) Therefore, we input a

View Document## MAT135H1 Lecture 38: Lecture Note

0

Riemann sums of the velocity given by the definite that change in position function integral can. Ha ) . then the change in position. Thus we have : be

View Document## MAT135H1 Lecture Notes - Lecture 37: Riemann Sum

0

At ) is from a individual continuous function for a et eb . We deride the into n to b subdivision. Ot so equal subdivisions and we call the width at be

View Document## MAT135H1 Lecture 36: Lecture Note

0

If ff? velocity is positive , the velocity curve . the total distance traveled is the area under. With time t in seconds the velocity of a bicycle in f

View Document## MAT135H1 Lecture Notes - Lecture 33: Chief Operating Officer

0

Find the global maximum and minimum of gtx) find critical fix ) the. 51/3 the the only critical critical point point and. 2x = yz in the the endpoint %

View Document## MAT135H1 Lecture 32: Lecture Note

0

Last we time we looked at talked about how to fix ) an example find local maxes i mins. 4343 . which of had functions two critical points. It nor turns

View Document## MAT135H1 Lecture 31: Lecture Note

0

Global maxima and minima are sometimes called extrema or optimal values. Global extrema are exist: then f has a global maximum and if f is continuous o

View Document## MAT135H1 Lecture Notes - Lecture 30: Parachuting

0

2cm per minute from an decreasing half an hour late ? is melting . Its radius decreases at a constant initial value of. The radius , t minutes since r

View Document## MAT135H1 Lecture Notes - Lecture 29: Maxima And Minima, Inflection

0

, p , inflection point of f . at which the graph of a continuous function f. Inflection point and local maxima and minima of the derivative . a. Suppos

View Document## MAT135H1 Lecture Notes - Lecture 28: Maxima And Minima, Thx

0

Connection t " f " f " f " 70 co between the derivative function and the. > 0 then interval on is t an function itself. increasing decreasing on the in

View Document## MAT135H1 Lecture Notes - Lecture 27: Linearization, Thx

0

Where: y are related but still we find ttx rules think of treat y x y as a and can"t we function of function and x and the derivative . In this type of

View Document## MAT135H1 Lecture Notes - Lecture 25: Thx, Fast Fourier Transform

0

[ flgcxs ) ] we saw how to take derivatives of composition of function flgcx )) g" cx ) had - I tex hlx ) et " (cid:15482) fix ) = ex. What happens if

View Document## MAT135H1 Lecture Notes - Lecture 23: Tonne, Product Rule, Thx

0

We saw we that talk about fix ) exponential the derivative of exponential function . f and f " are proportional (cid:12200) an. Temp between its object

View Document## MAT135H1 Lecture Notes - Lecture 22: Thx, Thomas Say

0

Derivative of far we there are start to a. Exponential functions really only know how to function which lot differentiate aren"t power functions useful

View Document## MAT135H1 Lecture Notes - Lecture 17: Thx

0

Have used the notation we f " to stand for the derivative of the variable y depends on the variable. X y = fix ) . we the function f . can write its so

View Document## MAT135H1 Lecture 15: Lecture Note

0

It does not mean time doesn"t move change at an change doesn"t it as on approximation of change change instant , happen . If we want of time to think o

View Document## MAT135H1 Lecture 14: Lecture Note

0

Last with a question trying we discussed viewing the derivative find a possible graph to thx ) for as fix ) a function we ended given fix ) - lnx - In

View Document## MAT135H1 Lecture Notes - Lecture 12: Ath, Constant Function

0

Feb 1st . the rate of change of a. Function f that depends on a variable we define other than time . Average rate of change of f over the interval from

View Document## MAT135H1 Lecture Notes - Lecture 11: Classical Mechanics, Special Relativity

0

Interval continuous b is is continuous a constant . f and is are g bfcx ) Fix) fix) gcx) fix ) i gtx) t g cx ) is continuous is continuous gcx) t o. X

View Document## MAT135H1 Lecture Notes - Lecture 10: Asymptote, Classical Mechanics

0

3 statement continuous in one tix ) exists tf"t fcc ) exists. Esc fix) is the same number as to. How can f function fail to be a not defined at c but c

View Document## MAT135H1 Lecture 6: Lecture Note

0

Last time we noticed the if fix ) log ax and gtx ) a then. The basics : special angles trig identities even. Pythoganten identities angles formula doub

View Document## MAT135H1 Lecture 5: Lecture Note

0

Logarithms turn exponential problems into linear ones y = ae lny - rx life) t la rx. la. Graphing a linear function has some advantages over graph , a

View Document## MAT135H1 Lecture 4: Lecture Note

0

Let fix ) be given by the table of values . Construct by a hlx ) fax ) table of values. X so hlz ) flu ) then input undefined is that into f. 14 doesn"

View Document## MAT135H1 Study Guide - Fall 2018, Comprehensive Term Test Notes - Confidence Trick, Francis Su, Calculator

0

## MAT135H1 Lecture Notes - Lecture 1: Ontario Human Rights Code, Francis Su, Maryam Mirzakhani

0

## MAT135H1 Study Guide - Midterm Guide: Hedeby Stones, Linearization, Transcendentals

0

Function-mapping that takes one input to one output. Example 1: your monthly rent fee is 1000$ a month input output. This is an example of many to one

View Document## MAT135H1 Lecture 1: Quick overview of Chap.1 and brief review of trigonometry ( appendix D)

0

## MAT135H1 Study Guide - Final Guide: Inverse Function, Special Economic Zone, If And Only If

78

## MAT135H1 Lecture Notes - Lecture 9: European Route E6, Automobilclub Von Deutschland, Yodh

43

## MAT135H1 Lecture 38: Lecture Note

0

Riemann sums of the velocity given by the definite that change in position function integral can. Ha ) . then the change in position. Thus we have : be

View Document## MAT135H1 Lecture Notes - Lecture 1: Inverse Function

0

Read sections 1. 1 -1. 5, appendix d from the textbook. An assignment that assigns a real number, and another real number, f ( ) Therefore, we input a

View Document## MAT135H1 Lecture 14: MAT135 - Lecture 14 - Chain Rule

0

Read sections 3. 4, 3. 5, and 1. 5 from the textbook. Suppose g is differentiable at and f is differentiable at g ( ). In leibniz notation, if = f ( u

View Document## MAT135H1 Lecture 16: MAT135 - Lecture 16 - Chain Rule Part Two

0

Mat135 - lecture 16 - chain rule part two. Suppose g is differentiable at and f is differentiable at g ( ). In leibniz notation, if = f ( u ) is differ

View Document## MAT135H1 Chapter Notes - Chapter 1.1: Even And Odd Functions, Piecewise

3

Mat135h1 f - calculus 8th edition (stewart) - section 1. 1. A function f assigns each value of x within the domain d exactly one value f x( ) within ra

View Document## Most Popular

Your classmatesâ€™ favorite documents.

## MAT135H1 Study Guide - Fall 2018, Comprehensive Term Test Notes - Confidence Trick, Francis Su, Calculator

0

## [MAT135H1] - Final Exam Guide - Everything you need to know! (46 pages long)

46 Page

1 Dec 2016

80

## Most Recent

The latest uploaded documents.

## MAT135H1 Lecture 38: Lecture Note

0

Riemann sums of the velocity given by the definite that change in position function integral can. Ha ) . then the change in position. Thus we have : be

View Document## MAT135H1 Lecture Notes - Lecture 37: Riemann Sum

0

At ) is from a individual continuous function for a et eb . We deride the into n to b subdivision. Ot so equal subdivisions and we call the width at be

View Document## MAT135H1 Lecture 36: Lecture Note

0

If ff? velocity is positive , the velocity curve . the total distance traveled is the area under. With time t in seconds the velocity of a bicycle in f

View Document