• Me
    Profile Supervise Logout
  •  Sign In
    Sign In with Google Sign In with Twitter Sign In with GitHub
Warning

You are about to erase your work on this activity. Are you sure you want to do this?

Updated Version Available

There is an updated version of this activity. If you update to the most recent version of this activity, then your current progress on this activity will be erased. Regardless, your record of completion will remain. How would you like to proceed?

 Delete my work and update to the new version.
Mathematical Expression Editor
[?]\blue{[?]}[?]

1Introduction: What is a limit?

1.1Stars at Night

Two young mathematicians discuss stars and functions.

1.2Geometric View of Limits

Visual introduction to Limits

1.3Geometric View - One Sided Limits

Visual introduction to One-sided Limits

1.6Analytic View - Tables

We discuss how to use tables to determine limits and the inherent danger to using this method.

1.7Limits: Notation, One-sided Limits, and Formal Definitions

We introduce the notation and formal algebraic definitions for limits.

2Limit laws

2.1Equal or not?

Here we see a dialogue where students discuss combining limits with arithmetic.

2.2The limit laws

We give basic laws for working with limits.

3Continuity and the Intermediate Value Theorem

3.1Roxy and Yuri like food

Two young mathematicians discuss the eating habits of their cats.

3.2Continuity

The limit of a continuous function at a point is equal to the value of the function at that point.

3.4Left/Right Continuity

The limit of a continuous function at an endpoint to determine continuity at endpoints.

3.5Continuity and Limit Laws

Here we see a consequence of a function being continuous.

3.7Continuity of piecewise functions

Here we use limits to check whether piecewise functions are continuous.

3.9The Intermediate Value Theorem

Here we see a consequence of a function being continuous.

4(In)determinate forms

4.1Could it be anything?

Two young mathematicians investigate the arithmetic of large and small numbers.

4.2Limits at Infinity

What does it mean to take a limit “At Infinity”?

4.3What Are Indeterminate Forms?

We introduce indeterminate forms and discuss what makes one form indeterminate compared to another.

4.4Limits of the form zero over zero

We want to evaluate limits for which the Limit Laws do not apply.

4.5Limits of the form nonzero over zero

What can be said about limits that have the form nonzero over zero?

5Using limits to detect asymptotes

5.1Zoom out

Two young mathematicians discuss what curves look like when one “zooms out.”

5.2Vertical asymptotes

We explore functions that “shoot to infinity” near certain points.

5.4Horizontal asymptotes

We explore functions that behave like horizontal lines as the input grows without bound.

6An application of limits

Some examples of application for limits, such as average and instantaneous rates of change.

6.1Limits and velocity

Two young mathematicians discuss limits and instantaneous velocity.

6.2Instantaneous velocity

We use limits to compute instantaneous velocity.
  1. mac2233limits
  2. Survey of Calculus One - Limits
  3. (In)determinate forms
  4. 902f8a…: “Towards a comfortable hummingbird”
    5. Jason Nowell
  • ← Previous
  • Next →

Start typing the name of a mathematical function to automatically insert it.

(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)

Controls

Press......to do
left/right arrowsMove cursor
shift+left/right arrowsSelect region
ctrl+aSelect all
ctrl+x/c/vCut/copy/paste
ctrl+z/yUndo/redo
ctrl+left/rightAdd entry to list or column to matrix
shift+ctrl+left/rightAdd copy of current entry/column to to list/matrix
ctrl+up/downAdd row to matrix
shift+ctrl+up/downAdd copy of current row to matrix
ctrl+backspaceDelete current entry in list or column in matrix
ctrl+shift+backspaceDelete current row in matrix
×

Start typing the name of a mathematical function to automatically insert it.

(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)

Symbols

Type......to get
norm∣∣[?]∣∣||\blue{[?]}||∣∣[?]∣∣
text[?]\text{\blue{[?]}}[?]
sym_name\[?]\backslash\texttt{\blue{[?]}}\[?]
abs∣[?]∣\left|\blue{[?]}\right|∣[?]∣
sqrt[?]\sqrt{\blue{[?]}}[?]​
paren([?])\left(\blue{[?]}\right)([?])
floor⌊[?]⌋\lfloor \blue{[?]} \rfloor⌊[?]⌋
factorial[?]!\blue{[?]}![?]!
exp[?][?]{\blue{[?]}}^{\blue{[?]}}[?][?]
sub[?][?]{\blue{[?]}}_{\blue{[?]}}[?][?]​
frac[?][?]\dfrac{\blue{[?]}}{\blue{[?]}}[?][?]​
int∫[?]d[?]\displaystyle\int{\blue{[?]}}d\blue{[?]}∫[?]d[?]
defi∫[?][?][?]d[?]\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}∫[?][?]​[?]d[?]
derivdd[?][?]\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}d[?]d​[?]
sum∑[?][?][?]\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}[?]∑[?]​[?]
prod∏[?][?][?]\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}[?]∏[?]​[?]
root[?][?]\sqrt[\blue{[?]}]{\blue{[?]}}[?][?]​
vec⟨[?]⟩\left\langle \blue{[?]} \right\rangle⟨[?]⟩
mat([?])\left(\begin{matrix} \blue{[?]} \end{matrix}\right)([?]​)
*⋅\cdot⋅
infinity∞\infty∞
arcsinarcsin⁡([?])\arcsin\left(\blue{[?]}\right)arcsin([?])
arccosarccos⁡([?])\arccos\left(\blue{[?]}\right)arccos([?])
arctanarctan⁡([?])\arctan\left(\blue{[?]}\right)arctan([?])
sinsin⁡([?])\sin\left(\blue{[?]}\right)sin([?])
coscos⁡([?])\cos\left(\blue{[?]}\right)cos([?])
tantan⁡([?])\tan\left(\blue{[?]}\right)tan([?])
secsec⁡([?])\sec\left(\blue{[?]}\right)sec([?])
csccsc⁡([?])\csc\left(\blue{[?]}\right)csc([?])
cotcot⁡([?])\cot\left(\blue{[?]}\right)cot([?])
loglog⁡([?])\log\left(\blue{[?]}\right)log([?])
lnln⁡([?])\ln\left(\blue{[?]}\right)ln([?])
alphaα\alphaα
betaβ\betaβ
gammaγ\gammaγ
deltaδ\deltaδ
epsilonϵ\epsilonϵ
zetaζ\zetaζ
etaη\etaη
thetaθ\thetaθ
iotaι\iotaι
kappaκ\kappaκ
lambdaλ\lambdaλ
muμ\muμ
nuν\nuν
xiξ\xiξ
omicronο\omicronο
piπ\piπ
rhoρ\rhoρ
sigmaσ\sigmaσ
tauτ\tauτ
upsilonυ\upsilonυ
phiϕ\phiϕ
chiχ\chiχ
psiψ\psiψ
omegaω\omegaω
GammaΓ\GammaΓ
DeltaΔ\DeltaΔ
ThetaΘ\ThetaΘ
LambdaΛ\LambdaΛ
XiΞ\XiΞ
PiΠ\PiΠ
SigmaΣ\SigmaΣ
PhiΦ\PhiΦ
PsiΨ\PsiΨ
OmegaΩ\OmegaΩ
×

Global settings:

Settings

×