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Calculus 1(A)
University of Toronto St. George
Verified Notes

Browse the full collection of course materials, past exams, study guides and class notes for MAT135H1 - Calculus 1(A) at University of Toronto St. George verified by our community.

PROFESSORS

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TBA

Mihai Nica

Melissa Lee Emory

Dimitri Chouchkov

Mayes-Tang S.

Richards L.

LeBlanc E.

Zerouali A.

Thaddeus Janisse

C Su

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Class Notes

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MAT135H1 Lecture Notes - Lecture 2: Francium, Exponential Growth

MAT135H1 Lecture 3: Lecture Note

MAT135H1 Lecture 4: Lecture Note

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"

MAT135H1 Lecture 5: Lecture Note

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

MAT135H1 Lecture 6: Lecture Note

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

MAT135H1 Lecture Notes - Lecture 7: Asymptote

MAT135H1 Lecture 8: Lecture Note

MAT135H1 Lecture 9: Lecture Note

MAT135H1 Lecture Notes - Lecture 10: Asymptote, Classical Mechanics

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

MAT135H1 Lecture Notes - Lecture 11: Classical Mechanics, Special Relativity

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

MAT135H1 Lecture Notes - Lecture 12: Ath, Constant Function

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

MAT135H1 Lecture Notes - Lecture 13: Thx

MAT135H1 Lecture 14: Lecture Note

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

MAT135H1 Lecture 15: Lecture Note

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

MAT135H1 Lecture Notes - Lecture 17: Thx

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

MAT135H1 Lecture Notes - Lecture 18: Thx, Power Rule

MAT135H1 Lecture Notes - Lecture 22: Thx, Thomas Say

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

MAT135H1 Lecture Notes - Lecture 23: Tonne, Product Rule, Thx

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

MAT135H1 Lecture Notes - Lecture 25: Thx, Fast Fourier Transform

[ 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

MAT135H1 Lecture Notes - Lecture 26: Inverse Function, Lego Mindstorms

MAT135H1 Lecture Notes - Lecture 27: Linearization, Thx

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

MAT135H1 Lecture Notes - Lecture 28: Maxima And Minima, Thx

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

MAT135H1 Lecture Notes - Lecture 29: Maxima And Minima, Inflection

, 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

MAT135H1 Lecture Notes - Lecture 30: Parachuting

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

MAT135H1 Lecture Notes - Lecture 31: Maxima And Minima

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

MAT135H1 Lecture 32: Lecture Note

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

MAT135H1 Lecture Notes - Lecture 33: Chief Operating Officer

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 %

MAT135H1 Lecture Notes - Lecture 34: Scale-Invariant Feature Transform, Thx

MAT135H1 Lecture Notes - Lecture 35: Thx

MAT135H1 Lecture 36: Lecture Note

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

MAT135H1 Lecture Notes - Lecture 37: Fax

MAT135H1 Lecture Notes - Lecture 38: Riemann Sum

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

MAT135H1 Lecture 39: Lecture Note

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