Calc I

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For Everyone, then these are for Math Teachers,
then these are for Math Teachers & Students

Projects

Project Tasks

Possible Projects

THE LIMIT FUNCTION - TAKE THE LIMIT AS X APPROACHES ...

fX.f'X.f''X.intX.gsp - THE DERIVATIVE & ANTIDERIVATIVE SKETCHPAD

CALC SUMMARY - still unfinished

DERIVATIVES
Function & Graph Analysis - instructions on how to find extremes and perdict the future

D(sin(x)) is cos(x)

Sketchpad, video, local video
First, a quick review of basic sine and cosine trig needed to prove D_x( sin(x) ) = cos(x). Proof by animated derivative of the slope of the tangent using a movable tangent line, then trace w/four derivatives of sine. Hand-written by-definition proof included. Presented from calc I class notes. Linked to a the downloadable SketchPad used in the video.

Derivative Rules & Additional Pages

Take a Derivative Using the Limit of the Difference Quotient

Function Emojis

Derivative Proofs d(e^x)/dx= e^x d( sin(x) )/dx = cos(x) d(f(x))/dx by definition

Implicit Differentiation

Related Rates

Inverse functions, derivatives of arc functions

Sine & Cosine

Use a Pencil to Take a Derivative or Antiderivative of Sine & Cosine Functions

Optimization Quiz Grading Rubric

SUMMATION
Summation Connect-the-dots Just Questions pdf
Summation Connect-the-dots Questions & Answers pdf

Summation Calculator
https:/goodcalculators.com/summation-calculator/

ANTIDERIVATIVES
Reimann Boxes & Sums, and Integration
Here's a Sample of the Reimann Sketchpad:
Within & Between in the "Center & Spread" Video
Beginning at 11:23 minutes into the video, and ending at 15:46 of the video, I used the ReimannSums.gsp to teach the probability of a score being within x standard deviations of the mean or to compute p( a < z < b).

Take an Antiderivative by Substitution

Integration Tricks/Techniques, including Using a Function in y rather than a Function in x

FTC, Fundamental Theorem of Calculus

CHEAT SHEETS & OTHER RESOURCES
T4 MAT131 Assorted Review Questions pdf

Calc Cheat Sheet -- Some derivatives, Trig and Hyperbolic Integrations, etc. in pdf format
page 1 in jpg format page 2 in jpg format page 3 in jpg format page 4 in jpg format

Connect-the-Dots in pdf Form Limits Derivatives Anti-derivative and Integral

Calc Calculators

Equation solving calculator
https://www.symbolab.com/solver/equation-calculator/

Graphing Tool
https://goodcalculators.com/graphing-calculator/

Applications Calculator
https://goodcalculators.com/

Derivative Calculator
https://www.derivative-calculator.net/

Summation Calculator
https://goodcalculators.com/summation-calculator/

Integral Calculator
https://www.integral-calculator.com/

Program Your TI84 Calculator to "Take a Derivative at a point or Evaluate a Definite Integral"

Other Resources Lectures & Videos
mathnstuff.com on video khanacademy.org/ (Doesn't use Internet Explorer. Use another browser.)
mathispower4u.com/calculus.php
myopenmath.com/, videos and problems w/answers
calcvids.org/vids/

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© 9/5/2025 A², Agnes Azzolino
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