In order to help students approach the basic tools to face calculus without major problems, we present where a list of useful links:
What is a function?
www.youtube.com/watch?v=PR5RUWpUY40
Domain and Range of a function:
https://www.youtube.com/watch?v=96uHMcHWD2E&list=PLSQl0a2vh4HCkRAK1wDAaesiYJVzNxXra&index=11
https://cubens.com/en/handbook/functions-and-graphs/domain-of-a-function
https://www.youtube.com/watch?v=6fDmLeS6Zzo
The Graph of the function:
https://cubens.com/en/handbook/functions-and-graphs/graph-of-a-function
Composition of Functions
https://www.youtube.com/watch?v=S4AEZElTPDo
Domain of Composite Functions
https://www.youtube.com/watch?v=G8r9oL-ke9s
Inverse Functions
https://www.youtube.com/watch?v=fK7IPeeZoFE
https://cubens.com/en/handbook/functions-and-graphs/inverse-function
How to find domain and range using inverse
https://www.youtube.com/watch?v=Veq5BBnfMPQ
Functions Exercises - Composite Functions and Inverse Functions
https://www.youtube.com/watch?v=1vS9DcKUkXw
Operations of Functions
https://www.youtube.com/watch?v=7N_-G4usp6Q&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=5
Even vs Odd Functions
https://www.youtube.com/watch?v=6897XAx3O9Q&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=8
Increasing vs Decreasing Functions
https://cubens.com/en/handbook/functions-and-graphs/increasing-and-nondecreasing-functions
https://www.youtube.com/watch?v=cIRDvscVPr0&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=9
Extrema of the function
https://www.youtube.com/watch?v=2hItEGb3KJo&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=10
Average Rate of Change of a Function
https://www.youtube.com/watch?v=H5Y-ONkezDM&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=11
Graphs You Must Know
https://www.youtube.com/watch?v=NrmmR3-VxA8&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=13
https://cubens.com/en/handbook/functions-and-graphs/properties-functions
Transformation of Functions
https://www.youtube.com/watch?v=sTCRB6hMsC4&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=14
https://www.youtube.com/watch?v=HkrMJLSpJFI&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=15
Linear Functions
https://cubens.com/en/handbook/functions-and-graphs/linear-function
https://www.youtube.com/watch?v=Ft2_QtXAnh8
https://www.youtube.com/watch?v=BtcKotD6Ni8
Linear-Fractional Function
https://cubens.com/en/handbook/functions-and-graphs/fractional-linear-function
Quadratic Formula
https://www.youtube.com/watch?v=KIWXZVsdpbE&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=21
Solving Quadratics
https://www.youtube.com/watch?v=mXAd6rkNSK0&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=17
https://www.youtube.com/watch?v=u2CFHYJWS60&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=18
https://www.youtube.com/watch?v=2BUg_w1Cu9E&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=20
Graphing Quadratic Functions
https://www.youtube.com/watch?v=VH4tzzBVbgA&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=24
Quadratic Inequalities
https://www.youtube.com/watch?v=qd41nGPHbMU&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=25
Polynomial Functions
https://www.youtube.com/watch?v=6Uh3Z6DJ_pI&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=27
Intersections of Functions
https://www.youtube.com/watch?v=2cXEuUazjCc&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=22
Substitutions to Solve Equations
https://www.youtube.com/watch?v=P8uoP-JFj54&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=23
Absolute value Functions
https://www.varsitytutors.com/hotmath/hotmath_help/topics/absolute-value-functions
Absolute value Inequalities
https://www.youtube.com/watch?v=SfImKHp094o
Asymptotes of the graph of a function
https://cubens.com/en/handbook/functions-and-graphs/asymptotes
Vertical Asymptotes - Rational Functions
https://www.youtube.com/watch?v=y-bSJaEonho&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=38
Horizontal Asymptote - Rational Function
https://www.youtube.com/watch?v=D-H9N-_Y77Y&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=40
Oblique Asymptote - Rational Function
https://www.youtube.com/watch?v=NVhaVk4wNu8&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=41
Graphing Rational Functions
https://www.youtube.com/watch?v=-k4uXF4hsAs&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=39
https://www.youtube.com/watch?v=wHATRiYbPPA&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=44
Inequalities with Functions
https://www.youtube.com/watch?v=bngBtS7RBZ4&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=45
Inequalities with Polynomial Functions
https://www.youtube.com/watch?v=qFJ-Mq0XcTI&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=46
Inequalities with Rational Functions
https://www.youtube.com/watch?v=QSh1xcbYKZk&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=47
Power Functions
https://www.youtube.com/watch?v=FXTlAPOBA_U&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=28
Exponential Functions Graphs
https://www.youtube.com/watch?v=2w14jBb0e9Q&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=52
https://www.youtube.com/watch?v=uycM-AzUDQ4&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=53
Exponential Equations
https://www.youtube.com/watch?v=FXTlAPOBA_U&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=29
Logarithms and Their Graphs
https://www.youtube.com/watch?v=jfnTwz79PWU&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=55
Graphing Logarithms with Transformations
https://www.youtube.com/watch?v=swC7KrDO0Uo&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=56
Solving Logarithms and Exponentials
https://www.youtube.com/watch?v=KezbqAAlOZk&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=57
Properties of Logarithms
https://www.youtube.com/watch?v=u0uScdsBPfk&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=58
https://www.youtube.com/watch?v=qCeN653SdX4&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=59
https://www.youtube.com/watch?v=YrU8fYchnIU&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=60
https://www.youtube.com/watch?v=tgcFt8zGnNE&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=61
https://www.youtube.com/watch?v=82fonULPl64&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=62
Limit of a function
Definition and Properties
https://cubens.com/en/handbook/algebra-and-introduction-to-mathematical-analysis/limit-of-a-function
Finding the limit using epsilon and Delta Definition
https://www.youtube.com/watch?v=dXr6aoJ1nVI
Evaluating Limits on a graph
https://www.youtube.com/watch?v=iCObJc5L8LM&list=RDCMUClOR1BiPyOkkIAnv9Cmj4iw&index=2
One-sided limits
Finding limits algebraically (using direct substitution and the conjugate)
https://www.youtube.com/watch?v=96DZt8YDohk
Indeterminate Forms
https://www.youtube.com/watch?v=oEEXnyupzdo
Remarkable trigonometric Limits (sin(x)/x, tan(x)/x)
https://www.youtube.com/watch?v=Dt8UTJL5XDY&t=558s
https://www.youtube.com/watch?v=QnSW3gsYXsM
https://www.youtube.com/watch?v=QnSW3gsYXsM
Remarkable Exponential and Logarithmic Limits ((e^(x)-1)/x, ln (x+1)/x, (1+(k/n))^n))
https://www.youtube.com/watch?v=98UZmqed3po&t=7s
https://www.youtube.com/watch?v=N8ZW7MT526A
Derivative of a Function
https://www.youtube.com/watch?v=962lLfW-8Jo
Techniques of Differentiation
https://www.youtube.com/watch?v=EY6FHX6asU0
https://www.youtube.com/watch?v=AvCQQ3X4Nuc
https://www.youtube.com/watch?v=RJJSiNz5oto
Continuous functions
https://www.youtube.com/watch?v=InDHwh1CvOg
Continuity of a Piecewise Functions
https://www.youtube.com/watch?v=SoMl89ZYJIg
Intermediate Value Theorem - Bolzano - Weierstrass theorem
https://www.youtube.com/watch?v=OEE5-M4aY4k&t=13s
https://www.youtube.com/watch?v=9wEHwFrUyOU&t=265s
First Derivative - Increasing and Decreasing Functions
https://www.youtube.com/watch?v=Dyl7jPlJXOM
First Derivative - Extrema of the function
https://www.youtube.com/watch?v=G5wlKltW7pM
Mean Value Theorem - Lagrange Theorem
https://www.youtube.com/watch?v=SL2RobwU_M4
Extreme value theorem - Weierstrass theorem
https://www.youtube.com/watch?v=Sx2lPZlnWfs
https://www.youtube.com/watch?v=ZsTipL3pIhY
Concavity, Inflection Points - Second Derivative
https://www.youtube.com/watch?v=15awMHeP1Yc
Concavity and Inflection Points - Example
https://www.youtube.com/watch?v=3TJLOCYrTes
Trigonometry
Introduction to angles
https://www.youtube.com/watch?v=c41QejoWnb4&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=74
Converting degrees, minutes and seconds
https://www.youtube.com/watch?v=U40Afn37QC4&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=75
Introduction to Radians
https://www.youtube.com/watch?v=EWd_FtOfyPc&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=76
Converting radians and Degrees
https://www.youtube.com/watch?v=sCwcbZSZL5o&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=77
Area of a sector, Angular velocity
https://www.youtube.com/watch?v=x6wnYbOBCic&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=78
Trigonometric Functions and the Unit Circle
https://www.youtube.com/watch?v=__nefjOhVks&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=79
Trigonometric Functions and the Unit Circle
https://www.youtube.com/watch?v=__nefjOhVks&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=79
How to Use the Unit Circle in Trigonometry
https://www.youtube.com/watch?v=GdRZfemxTFI&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=80
Basic Properties of Trigonometric Functions
https://www.youtube.com/watch?v=_dTRpq_yGIc&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=81
Reciprocal Identities in Trigonometry
https://www.youtube.com/watch?v=98jDUsZ2JYA&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=82
Pythagorean Identities for Trigonometric Functions
https://www.youtube.com/watch?v=huP3v7iZuLM&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=83
The Graphs of Sine and Cosine
https://www.youtube.com/watch?v=3HHgZopzL_s&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=84
Graphing Transformations with Sine and Cosine
https://www.youtube.com/watch?v=dyXT5KMCrPk&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=85
How to Graph Tangent and Cotangent
https://www.youtube.com/watch?v=8eMEBrPYJ0I&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=86
Graphing Transformations with Tangent and Cotangent
https://www.youtube.com/watch?v=i4rr_J1VbkY&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=87
How to Graph Cosecant and Secant
https://www.youtube.com/watch?v=kYIKNTXaf_E&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=88
How to Graph Phase Shifts of Trigonometric Functions
https://www.youtube.com/watch?v=bE5PFI-ibT8&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=89
Introduction to Inverse Trigonometric Functions
https://www.youtube.com/watch?v=ih01YszlraY&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=90
How to Use Inverse Trigonometric Functions
https://www.youtube.com/watch?v=6PB76VMNiX0&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=91
How to Find Inverse Trigonometric Functions
https://www.youtube.com/watch?v=Ru9Xbd01Jk8&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=92
How to Solve Basic Inverse Trigonometric Functions
https://www.youtube.com/watch?v=PEwUFrx-vPA&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=93
An In-depth Look at Using Inverse Trigonometric Functions
https://www.youtube.com/watch?v=1f6BhHlkgy4&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=94
How to Solve Trigonometric Equations
https://www.youtube.com/watch?v=hBk7OnEYPcw&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=95
Introduction to Using Trigonometric Identities
https://www.youtube.com/watch?v=yIMR-3c1wP8&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=96
How to Prove Trigonometric Identities
https://www.youtube.com/watch?v=az_veh1FLbo&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=97
Introduction to Sum and Difference Formulas in Trigonometry
https://www.youtube.com/watch?v=9R5Nz1eYddM&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=98
Using Sum and Difference Formulas in Trigonometry
https://www.youtube.com/watch?v=xw4HLT3TmIU&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=99
Proving the Double and Half Angle Formulas for Trigonometry
https://www.youtube.com/watch?v=Epa2mi8hzBA&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=100
How to Use the Double and Half Angle Formulas for Trigonometry
https://www.youtube.com/watch?v=Pf6p6lCs5I8&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=101
How to Use Product to Sum and Sum to Product Formulas in Trigonometry
https://www.youtube.com/watch?v=tHdcvWNNXZE&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=102
Introduction to Right Triangle Trigonometry
https://www.youtube.com/watch?v=Sy_ZCtD2tWo&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=103
Finding Sides and Angles with Right Triangle Trigonometry
https://www.youtube.com/watch?v=OHiZDKUwlQ4&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=104
How to Use the Law of Sines in Trigonometry
https://www.youtube.com/watch?v=-izzbKILEM0&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=105
How to Use the Law of Cosines in Trigonometry
https://www.youtube.com/watch?v=HOI_PnFG67Q&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=106
How to Find the Area of a Triangle with Trigonometry
https://www.youtube.com/watch?v=_i9t-ldjG7o&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=107
Graphing Trigonometric Functions
https://www.youtube.com/watch?v=SzLF-wLZF_I
Finding Derivatives of Trigonometric Functions