135 -- Comparison

135 -- Comparison and bounding with ln(n)

135 -- Positive series and monotonic convergence

135 -- Bounded monotonicity and series

135 -- Partial fractions and telescoping series

135 -- Telescoping Series

135 -- Long division and partial fractions

135 -- Integral test for 1/(n^2+4)

135 -- Integral test for n^2e^{-n^3}

135 -- Zeta(Odd) is open

135 -- Integral test and the zeta function

135 -- Riemann zeta function

135 -- Integral test

135 -- Integrals and sums

135 -- Divergence test

135 -- Simple divergent sequence

135 -- Examples of convergence and divergence

135 -- Sequences vs series

135 -- Geometric series

135 -- Sequences and series

133 -- Seperable with initial condition

133 -- General strategy for seperable equations

133 -- Seperable equation dy/dx = e^(3x-y)

133 -- Seperable equations

133 -- General strategy for simple differential equations

133 -- Solving a simple differential equation with an intitial condition

133 -- Simple differential equations

133 -- Definition of differential equation

133 -- Differential equations ("How far?")

135 -- Series vs integrals

135 -- Divergence test

135 -- Sequence vs Series

135 -- Sequences and series

135 -- Geometric series and two cups of tea

135 -- Infinite polynomials and geometric series

135 -- Geometric series

135 -- Sequences and logarithms

135 -- Factorials cancelling

135 -- Limit using logs (2)

135 -- Limit using logs (1)

135 -- Convergence of sequences

135 -- Geometric series and comparison

135 -- Partial sums of geometric series

135 -- Geometric series

135 -- Sequences and logarithms

135 -- Factorials

135 -- Examples of monotonic/bounded sequences

135 -- Increasing / Decreasing / Monotonic / Bounded

135 -- Squeeze theorem

135 -- Geometric sequences

135 -- Deep Theorem: bounded + monotonic ==> convergent

135 -- Boundedness

135 -- Monotonicity

135 -- Factorials

135 -- Squeeze theorem for zero limits

135 -- Convergence of r^n

135 -- Divergence / Convergence using graphs

135 -- Extending a sequence to the real numbers

135 -- Sequences are like functions

133 -- Horizontal slices

133 -- Two interpretations of area between curves

133 -- Area between curves

133 -- Complicated Area (2)

133 -- Complicated Area (1)

133 -- Integration geometrically

133 - Signes / Total area

133 -- Area and Integrals

135 -- Geometric series

135 -- Sequences are like functions

135 -- Divergence to infinity

135 -- Convergence / Divergence of sequences

135 -- Finding a formula

135 -- Examples of sequence

135 -- Sequences

135 -- Comparison

135 -- Comparison

135 -- Comparison for integrals

135 -- Comparison for integrals

135 -- Improper integrals at end points

135 -- Improper integrals around asymptotes

135 -- Improper integrals around asymptotes

135 -- Why do we need two limits?

135 -- Two sided improper integrals

135 -- p-test in general

135 -- p-test at p=1

135 -- p-test generally

135 -- Lead up to p-test

135 -- Improper integrals

135 -- Integral of 1/(1+e^x) part (2)

135 -- Integral of 1/(1+e^x) part (1)

135 -- Summary of partial fractions

135 -- Fundamental Theorem of Real Algebra

135 -- Repeated linear terms

135 -- Multiplying with repreated linear terms

135 -- Long division of polynomials

135 -- Dividing with beans

135 -- Partial fractions with irreducible quadratic factors

135 -- Partial fractions decomposition with a repeated linear factor

135 -- Integration using partial fractions

135 -- Partial fractions

135 -- Partial fractions

135 -- Long division (x^4+1)/(x-1)\

135 -- Checking a division of polynomials

135 -- Long division of polynomials

135 -- Long division of integers

133 -- Same slopes.

133 -- Derivatives and Anti-Derivatives

133 -- FTC Example

133 -- Exact Area and Fundamental Theorem of Calculus

133 -- L(f) and R(f) (2)

133 -- L(f) and R(f) (1)

133 -- Left endpoint sums

133 -- Riemann sum setup (3)

133 -- Riemann sum setup (1)

133 -- Riemann sum setup (2)

135 -- Area of circle by trig substitution (2)

135 -- Area of circle by trig substitution (1)

135 -- Different frequencies example

135 -- Different frequencies example

135 -- Different frequencies

135 -- Degree reduction (2)

135 -- Degree reduction (1)

135 -- Strategy for even powers

135 -- General strategy for odd powers

135 -- Trig integral (2)

135 -- Trig integral (1)

135 -- Direct substitution

135 -- Trig integral topics

135 -- Trig substitution for sqrt(x^2+4)

135 -- Integral of sec(x) and trig substitution for sqrt(x^2-1)

135 -- Table of trig substitution resemblences

135 -- Trig substitution for sqrt(1-x^2)

135 -- Resemblence of square roots

135 -- General strategy for odd powers

135 -- Non-obvious parts

135 -- Iterated parts (4)

135 -- Iterated parts (3)

135 -- Iterated parts (2)

135 -- Iterated parts (1)

135 -- Integration by parts formula

135 -- Idea behind integration by parts

135 -- Max/min and average

135 -- Riemann sums and averages

135 -- Finding n in a Riemann sum

135 -- Integration and products

133 -- Critical points

133 -- Local max/min example

133 -- Optimization

133 -- Implicit differentiation

133 -- Implicit differentiation split

133 -- Implicit differentiation idea

133 -- Implicit differentiation

135 -- Cavalieri's princple

135 -- Volume of rotation with boundary split (2)

135 -- Volume of rotation with boundary split (1)

135 -- Volume of rotation about y=1

V135 -- Colume of rotation about y-axis

135 -- Volume of rotation

135 -- Volume of rotation

Math Circles -- Geometry (10)

Math Circles -- Geometry (9)

Math Circles -- Geometry (8)

Math Circles -- Geometry (7)

Math Circles -- Geometry (6)

Math Circles -- Geometry (5)

Math Circles -- Geometry (4)

Math Circles -- Geometry (3)

Math Circles -- Geometry (2)

Math Circles -- Geometry (1)

135 -- Rotating around y-axis (5)

135 -- Rotating around y-axis (3)

135 -- Rotating around y-axis (2)

135 -- Rotating around y-axis (1)

135 -- Rotating bounded regions (2)

135 -- Rotating bounded region (1)

135 -- Volume of sphere (2)

135 -- Volume of sphere (1)

135 -- Body of Revolution

135 -- Volume of cone (3)

135 -- Volume of cone (2)

135 -- Riemann disks

135 -- Inner/outer regions (3)

135 -- Inner/outer regions (2)

135 -- Inner/outer regions (1)

135 -- Volume of a sphere (2)

135 -- Volume of sphere (1)

135 -- Volume of revolution formula

135 -- Volume of a cone

135 -- Volume and Riemann

135 -- Horizontal slices with bound

135 -- Horizontal slices with bound

135 -- Horizontal slices example

135 -- Horizontal slices algorithm

135 -- Horizontal strips example

135 -- Horizontal strips

135 -- Volume and Riemann disks

135 -- Horizontal and vertical slices

135 -- Horizontal and vertical slices

135 -- Area function of a piecewise function (3)

135 -- Area function of a piecewise function (2)

135 -- Area function of a piecewise function (1)

135 -- Area between curves with symmetry

135 -- Area between curves with symmetry

135 -- Area between curves

135 -- Signed and total area

135 -- Negative area

135 -- Riemann sum and definite integrals

133 -- Implicit differentiation and inverses

133 -- Implicit differentiation and the inverse of y=e^x

133 -- Implicit differentiation and inverses

133 -- Implicit differentiation

133 -- Implicit differentiation

133 -- Putting the pieces together

133 -- Slope of x^2

133 -- Slope of x^x

133 -- Logarithmic Differentation: Split up the function

133 -- Logarithmic Differentiation (2)

133 -- Logarithmic differentiation (1)

Math Club -- Number Theory: long lists of composites

Math Club -- Number Theory: congurence and repunits

Math Club -- Number Theory: infinitude of primes

Math Club -- Number theory: sqrt(2) is irrational

Math Club -- Number theory

135 -- Horizontal and vertical slices

135 -- Top and Bottom Curves

135 -- Signed and Total Area

135 -- Negative Area

135 -- Cancellation of "+C"

135 -- Working out bounds

135 -- Substitution and trigonometry

135 -- Substitution and look-alikes

135 -- Substitution with bounds

135 -- Net change and growth

135 -- Net change and distance

135 -- Area and definite integrals

135 -- Substitution with bounds

135 -- Substitution formula

135 -- Exploring subsitution

135 -- Net Change and speed

135 -- Net Change and constant speed

135 -- Net change formula

135 -- Area and definite integrals

135 -- Antiderivative of 1/(1+x^2)

135 -- Indefinite integrals

135 -- Antiderivative of b^x

133 -- Tables of values

133 -- Three step chain rule

133 -- Identifying chains

133 -- Chains of functions

133 -- The Chain Rule (with colour!)

133 -- The Chain Rule

133 -- The Chain Rule

Math Club -- Geometry 5

Math Club -- Geometry 4

Math Club -- Geometry 3

Math Club -- Geometry 2

Math Club -- Geometry 1

135 -- Simplifying ratio of trig

135 -- sec^2(x) and sec(x)tan(x)

135 -- Evaluating a definite integral

135 -- Table of anti-derivatives

135 -- Definite and Indefinite Integrals

135 -- FTC1 and bounds

135 -- FTC 1 and bounds

135 -- FTC and "+C"

135 -- Guess and Check

135 -- Anti-derivatives

135 -- Fundamental Theorem Parts 1 and 2

135 -- Mix/Max bounds

135 -- The Reimann sum

133 -- n'th derivative of 1/x

133 -- n'th derivative of x^n

133 -- Higher order derivatives

133 -- Quotient rule

133 -- Product rule

133 -- Product rule example

133 -- Power rule

133 -- Leibniz notation

133 -- Tangent line #2

133 -- Tangent line #1

133 -- Definition of derivative

135: Alice and Bob walk away

135: Related rates steps

135: Growing circle

135: Idea of related rates

135: Newtonian turkey

135: Growth / Decay / Heating / Cooling

135: Filling a cylinder

135: Growing circle 1

135: Growing circle 2

135: Newtonian turkey

133: Three heads in six tosses

133: Outcomes of six tosses

133: Unfair dice

133: Output even on unfair dice

133: Exclusive events

133: Equiprobable

133: Probability distribution

133: Sample space

135: Population triples

135: Population growth

135: Natural growth law

232: Converting to polar coordinates

232: Area as volume

232: Area as volume (integrate 1dA)

232: Volume of prism

232: Volume in polar coordinates

232: Volume in polar coordinates

232: Geometry word problem

Problem Solving Circle

Problem Solving Circle

135: Logarithmic differentiation

135: The chain!

135: Differentiating log_10

232: Volume of first octant sphere

232: Volume in polar coordinates

232: Regions in space / first octant

232: Sketching regions and substitution

232: Integral over triangle in two ways

232: Integral over triangle

135: Domain and range of ln(ln(ln(x)))

135: Higher order implicit

135: Derivative of x^x

135: Constants and product rule

135: Derivative of log_b(x)

135: Derivative of cos^{-1}(x)

135: Chain rule

135: Derivative of ln(|x|)

135: Derivative of ln(x)

135: sin(sin^{-1}(x)) = x

135: Colourful chain rule

135: Implicit sqrt(x+y) = x^4 + y^4

135: Idea of implicit differentiation

135: Implicit differentiation

133: Lunch combos

133: Two question multiple choice randomly

133: Multiple choice randomly

133: Multiple choice randomly

133: Seven on two dice

133: Probability and Counting

135: Implicit differentiation introduction

133: Eigenvector example

133: Determine all x such that M(x) is invertible

133: Determine all x such that M(x) is invertible

133: Cofactor expansion formula

133: Cofactor expansion

133: Determinant of 3x3

133: Determinant of 2x2

133: Does this matrix have an inverse?

133: Determine inverse of a matrix

232: Limit of y^2sin(x)/(3x^2+y^4)

232: Limit at the origin

232: Arclength of r(theta)=theta^2

232: 13.8.5 Points closest to the origin

232: Splitting a constraint in to Lagrange and Hess

232: Hessian and Lagrange

232: Lagrange multipliers

135: Invert a function

135: 1/(1+e^(1/x))

135: S3.1Q56 When does e^x - 2x have a horizontal tangent

135: Derivative of f(x)=2^x

135: Point slope format

135: S3.1Q63 Find two tangents

135: Tangent line

135: S3.1Q67 Find a quadratic ...

135: Derivative of a polynomial

135: Power rule

135: Derivative is additive

133: Solving a linear system with variables

133: Largest number of parameters

133: Smallest number of parameters

133: Rank and Parameters

133: RREF Algorithm

133: Solving a system with two parameters

133: Solving a system with two parameters

133: Examples of RREF

133: Matrices and Rank

232: Constrained optimization

232: Lagrange multipliers

232: Unconstrained optimization

135: Leibniz notation

135: Higher-order derivatives

135: Relationship between f(x) and f'(x) for polynomials

135: Graphing y=x^3 - 3x

135: The Derivative as a Function

135: Differentiable => Continuous

135: Visually |x| is not differentiable

135: |x| is not differentiable

135: 2x+3 is differentiable

135: Differentiable

232: Maximizing the surface area of a box

232: Second derivative test

232: cups, caps, and saddles

232: Hessian matrix examples

232: Hessian Matrix

232: Critical points

232: Clairaut's Theorem

232: Higher order partials

232: Higher order partial derivatives

135: Power rule and chain rule

135: Derivative of 4/sqrt(1-x)

135: Limit definition of derivative

135: Tangent to sqr(x+1) at x=3

135: Tangent to x^2 at x=1

135: Tangent lines

135: Secant lines

135: Derivatives and rates of change

135: Horizontal asymptotes

135: Limit to infinity sqrt(2x^2 + 1)/(3x+7)

135: Limit to infinity sqrt(x^2+1)-x

135: Divide by highest power

135: Numerical example of limit to inifinity

135: Limits to infinity

135: IVT and S2.5Q55

135: How do we use IVT?

133: Infinitely many solutions vs Unique solution

133: Row operations 2

133: Row Operations 1

133: Row operations

133: Shape of unique solution

133: Matrix form of a system

135: Horizontal asymptotes

135: Limits to infinity

135: Limits to infinity

135: S2.5Q55 IVT

232: What maximizes df/du?

232: Homework 13.5.6

232: Directional derivatives and slope

232: Directional derivative and gradient

232: Directional derivative example

232: Directional derivative example

232: Directional derivatives from the chain rule

232: Directional derivatives

232: Directional derivatives

135: Continuity and travel

135: Continuity and travel

135: IVT and cos(theta)=1/pi

135: Intermediate Value Theorem

135: Left vs Right

135: Left vs Right

135: Left and right continuity

135: Homework S2.5Q45

135: Homework S2.5Q45

135: Continuity example 1

135: Continuity example 1

135: Continuous at x=a

135: "What makes this discontinuous?"

135: "What makes this discontinuous?"

232: Implicit partial differentiation

232: Composing vs the Chain Rule

232: Chain rule

232: Tangent plane example 2

232: Tangent plane example 1

232: Tangent plane

232: Partial derivative examples

232: Difference quotient in two variables

232: Partial derivatives

133: Bond Example1

133: Bond example 1

133: Perpetuity

133: Present value of an annuity

133: Present value diagram

133: Present value

133: Annuity of 2000\$/mo with 6% APR monthly

133: Annuities with APR interest

133: Geometric series and annuities

133: Calculating the value of annuity

135: One sided limits graphically

135: One sided limits

232: Limit of x^2 + y^2

232: Contuinity

232: List of paths

232: Limit of (xy^2)/(x^2 + y^4)

232: Limits and parametrized paths

232: Limits and continuity

232: Cross sections of f(x,y) = |x| + |y|

232: Level sets of x^2 - y^2

232: Cross sections

232: Level curves

232: Functions of several variables

232: Parametric equations in space

232: Unit vectors

232: Normal of a plane

232: Lines and planes

135: sin^{-1}(sin(t))

135: sin^{-1}(sin(t))

135: sin(cos^{-1}(t))

135: Inverse cos of sqrt(3)/2

135: Restricting domain of trig functions

135: Trig and horizontal line test

135: Homework SAppDQ65

135: Homework SAppDQ29

135: Homework SAppDQ29

135: pi/3 special triangle

135: pi/4 special triangle

135: Convert pi/4 in to degrees

135: Radians and degrees

135: Trigonometry

135: Domain of ln(1-sqrt(x))

135: Domain of ln(x^2 - 16)

133: Simple compound interest

133: Value of investment at 2 years (ex.1)

133: Value of investment at 1 year. (ex.1)

133: Compound interest (ex.1)

133: Compound interest

133: Compound interest

133: Geometric series from k=100

133: Geometric series from k=3

133: The grains of rice myth

133: Geometric series with r=1/2

133: Geometric series

133: Sigma notation

135: The special triangles

135: Degrees to radians

135: Definition of radian

135: Radians and degrees

135: Trigonometry

135: Homework S1.5Q16

135: Domain of ln(1-sqrt(x))

135: Union notation

135: Invesrse functions and exponentials

135: exp(x) and ln(x) are inverses

232: Arclength of parametric cuvres

232: Orientation and parametic curves

232: Parametric equations

135: Homework S1.5Q15

135: ln(x) is the inverse of exp(x)

135: Solving exp(7-4x)=6

135: Properties of ln(x)

135: Natural logarithm

135: Checking an inverse

135: Inverse of f(x)=2x+1

135: Inverse functions

135: Vertical line test

135: Horizontal line test

135: Examples of one-to-one

135: One-to-one functions

232: Slope of parametric cuvres

232: The cycloid curve

232: Parametric equations

232: Area between polar curves

232: Area between polar curves

232: r=sin(3theta) and r=sin(2theta)

135: Absolute values

135: Simplifying using logarithms

135: Solving exp(7-4x)=6

135: Inverting f(x)=2x+1

135: Inverses and logarithms

135: Simplifying exponential expressions

135: Transforming an exponential

135: Translating exponentials

135: Graphing exponentials

135: Simplifying exponential expressions

135: Exponential functions

135: Inverse functions f(x)=x^3 + 1

133: Inverse functions

133: Logarithm facts

133: log(ab) = log(a) + log(b)

133: loog_10(1000)

133: n'th roots

133: Graph of y=2^x

133: Exponential functions

135: Horizontal stretches / compressions

135: Vertical stretches / compressions

135: Vertical stretches

135: Horizontal shifts

135: Horizontal shifts

135: New Functions from Old

135: Essential functions

232: Area of Flower

232: Area in Polar Coords

Area in Polar Coordinates