Mathorama
128 episodes - English - Latest episode: 10 months ago - ★★★★★ - 1 ratingCalculus and other math problems explained
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Episodes
Summer Topic: Domains
July 12, 2023 14:24 VideoNot all functions can take any number. The set of numbers that the function can accept is called a domain. Here we review how to analyze a function to find its domain.
Some Algebra of Calculus
August 05, 2022 16:55 VideoSome Algebra of Calculus Before Calculus you used Algebra to solve for x. Now in Calculus we use Algebra to manipulate an expression to make for easy Calculus!
Volume of a Solid (Washer method) Example.
February 19, 2022 19:40 VideoHow to use a TI-84 to find the volume of a hollow solid (which is ofter referred to "the washer" method since our circular cross-sections will have a hole in them. Others prefer the name "annular disk" or "ring" SFHS students can follow this link: https://www.deltamath.com/app/assignment/15468561 Everyone can download a pdf at mathorama.com
Intro to Volumes of Revolution: Disk Method
February 19, 2022 17:38 VideoAn introduction to finding the Volume of a solid generated by rotating an area around a line. Everyone can download a pdf at mathorama.com
More definite Integrals and Area under a Curve (4.4 p 293 # 62)
December 02, 2021 19:40 VideoMore Definite Integrals and the Area Under a Curve (4.4 p 293 # 62) With just a little information about the area of some regions, we can use the properties of integrals to figure out 6 different things!
MVT for Integrals, 1st FTC, and 2nd FTC Proofs
November 26, 2021 21:46 VideoMVT for Integrals, 1st FTC, and 2nd FTC Proofs Section 4.4 is chock full of gold. There is a lot there, so the video lets you take it in. Here are the Subjects by Time: 0:00 - The MVT for integrals (Average Value Thm) & AVERAGE VALUEs 4:20 - An example with f(x) =6 and a curious observation 6:24 -The First Fundamental Theorem Proof 11:16 - An Example of FTC1 12:51 - "Net Change Theorem" version of FTC1 with a "word problem" example 15:27 -The Second Fundamental Theorem of Calc...
Related Rated Samples
October 17, 2021 17:41 VideoRelated Rates Example Problems Here are 7 examples of Related Rates problems.
Using L'Hôpital's Rule on an e^x Function
February 04, 2021 03:01 VideoUsing L'Hôpital's Rule on an e^x Function
Inverse Functions Have Reciprocal Slopes (5.R p 400 #39)
February 04, 2021 01:27 VideoInverse Functions Have Reciprocal Slopes (5.R p 400 #39)
A u-sub for arctan (5-R p. 400 #109)
February 04, 2021 00:06 VideoA u-sub for arctan (5-R p. 400 #109)
A Hybrid Parametric Area with d(theta) (10-R p.747 #57)
February 03, 2021 22:40 VideoA Hybrid Parametric Area with d(theta) (10-R p.747 #57)
Elliptical Orbit in a Polar Form (10.6 p745 #59)
February 02, 2021 05:16 VideoElliptical Orbit in a Polar Form (10.6 p745 #59) Not only do we answer the question at hand, we derive the polar form of a conic section. If you want to skip ahead: Minute 5:45 Finding the distance between the surface of Earth and Explorer 18 when the angle is 60 degrees Minute 12:53 Proof that e = c/a = 2c/2a=(distance between focii/major axis)
Definite Integral with arcsine (5.8 p387 #33)
February 02, 2021 04:56 VideoDefinite Integral with arcsine (5.8 p387 #33)
Finding a Tangent Line Implicitly on a function with e^x (5.4 p348 #65)
February 02, 2021 04:42 VideoFinding a Tangent Line Implicitly on a function with e^x (5.4 p348 #65)
Implicit Differentiation with e^x (5.4 p 348 #63)
February 01, 2021 18:00 VideoImplicit Differentiation with e^x (5.4 p 348 #63)
Verifying a Differential Equation involoving e^x (5.4 p349 #69)
February 01, 2021 17:44 VideoVerifying a Differential Equation involoving e^x (5.4 p349 #69)
A Bounded Area (def Int) with log base 4 (5.5 p359 #81)
February 01, 2021 03:03 VideoA Bounded Area (def Int) with log base 4 (5.5 p359 #81) This one has u substitution a a conversion from base 4 to bas e, confirming with the TI-84
An Indefinite Integral with Exponents (5.5 p 359 #76)
February 01, 2021 00:08 VideoAn Indefinite Integral with Exponents (5.5 p 359 #76) This includes u-substitution, and an exponential function in base 2
Derivative of a Log in base 2 (5.5 p358 #55)
January 31, 2021 23:53 VideoDerivative of a Log in base 2 (5.5 p358 #55)
Proving an old Compounded Interest Formula with L'Hôpital's Rule (5.6 p371 #90)
January 31, 2021 23:40 VideoProving an old Compounded Interest Formula with L'Hôpital's Rule (5.6 p371 #90) We demonstrate the ln technique as well as makeing a product into a ratio so you can use L'Hôpital's Rule.
Implicit Diff with arctan (5.7 p 380 #71)
January 31, 2021 22:49 VideoImplicit Diff with arctan (5.7 p 380 #71) Here we find a tangent line of a function using implicit differentiation, the product rule, the chain rule, and some careful algebra.
Derivatives of Inverse Functions on the TI-84 (5.3 p 340 #71)
January 31, 2021 22:01 VideoDerivatives of Inverse Functions on the TI-84 (5.3 p 340 #71)
The Derivative of an Inverse Function (5.3 p340 #67)
January 31, 2021 21:38 VideoThe Derivative of an Inverse Function (5.3 p340 #67) The derivative of a inverse function is the reciprocal of the derivative of the inverse function. Be mindful of the exchange of values (x,y) to (y,x) with inverse functions
Intersections of Polar Curves (10.5 p 735 #29)
January 31, 2021 21:17 VideoIntersections of Polar Curves (10.5 p 735 #29)
Limiting the Domain of a Absolute Value Function so it would have an inverse (5.3 p340 #57)
January 25, 2021 03:33 VideoLimiting the Domain of a Absolute Value Function so it would have an inverse (5.3 p340 #57)
Inverse Functions (5.3 p 340 #53)
January 24, 2021 19:14 VideoInverse Functions (5.3 p 340 #53) We have more than just the horizontal line test now, if a function is strictly monotonic, it will have an inverse.
Celsius/Fahrenheit Inverse Functions (5/3 p 340 #50)
January 24, 2021 18:11 VideoCelsius/Fahrenheit Inverse Functions (5/3 p 340 #50)
Review of a Midpoint Riemann Sum (5.2 p 331 #77)
January 24, 2021 16:20 VideoReview of a Midpoint Riemann Sum (5.2 p 331 #77)
The Area of a Region That Involves a Secant Function (5.2 p331 #71)
January 24, 2021 15:39 VideoThe Area of a Region That Involves a Secant Function (5.2 p331 #71)
Another Definite Integral without u-Substitution (5.2 p 331 #65)
January 23, 2021 17:56 VideoAnother Definite Integral without u-Substitution (5.2 p 331 #65)
A Definite Integral Requiring u-Substitution (5.2 p 330 #51)
January 23, 2021 17:33 VideoA Definite Integral Requiring u-Substitution (5.2 p 330 #51)
Another Slope Field and Differential Equation with Natural Logs (5-2 p330 #50)
January 20, 2021 16:04 VideoAnother Slope Field and Differential Equation with Natural Logs (5-2 p330 #50)
Slope Fields and Differential Equations with Natural Logs (5-2 p330 #49)
January 20, 2021 15:45 VideoSlope Fields and Differential Equations with Natural Logs (5-2 p330 #49) A slope field and a diffyQ checked with the TI-84
A u-Sub Involving Natural Log ln x (5-2 p330 #49)
January 20, 2021 15:38 VideoA u-Sub Involving Natural Log ln x (5-2 p330 #49)
Long Division AND u-Substitution help this Integral (5-2 p330 #21)
January 19, 2021 18:04 VideoLong Division AND u-Substitution help this Integral (5-2 p330 #21)
Long Division Before Integrating (5-2 p330 #17)
January 19, 2021 17:41 VideoLong Division Before Integrating (5-2 p330 #17) This one looks like a difficult u-sub, but turns out to be easy after long division!
Differentiating Using Logarithms Instead of the Quotient Rule (5-1 p322 #79)
January 19, 2021 17:00 VideoDifferentiating Using Logarithms Instead of the Quotient Rule (5-1 p322 #79)
A Tangent Line Confirmed with the TI-84 (5-1 p322 #69)
January 11, 2021 23:46 VideoA Tangent Line Confirmed with the TI-84 (5-1 p322 #69) We confirm our result with the (DRAW)(5:Tangent) feature on the TI-84
Taking the Derivative of a Log Function (5-1 p322 #55)
January 11, 2021 22:34 VideoTaking the Derivative of a Log Function (5-1 p322 #55) We use the quotient rule together in this example.
U-substitution with a Definite Integral (4-R p310 #67)
January 11, 2021 18:51 VideoU-substitution with a Definite Integral (4-R p310 #67) When you use u-substitution with a definite integral, you don't have to switch back to make an expression in terms of x. Since any definite integral is the signed area, it is just a number. After finding the anti-derivative in terms of you, the FTC can be used to arrive at the answer.
Using the u-substitution Technique with an Indefinite Integral (4-R p301 #59)
January 11, 2021 16:05 VideoUsing the u-substitution Technique with an Indefinite Integral (4-R p301 #59) A basic example of how to integrate something that looks like a product, where one factor has something in common with the derivative of the other factor.
Basic Use of the First Fundamental Theorem (4-R p 310 #41)
January 11, 2021 15:41 VideoBasic Use of the First Fundamental Theorem (4-R p 310 #41) Here we use the First Fundamental Theorem of Calculus to evaluate a definite integral, and we will check our work with a TI-84 calculator,
Riemann Sums to Estimate an Integral (4-R p 309 #25)
January 11, 2021 15:20 VideoRiemann Sums to Estimate an Integral (4-R p 309 #25) Here we use left and right Riemann sums to get the upeer and lower bounds on an integral. We can then use the TI-84 to check our work.
Mean Value Theorem for Integrals with the TI-84 (4-5#85)
January 10, 2021 16:57 VideoMean Value Theorem for Integrals with the TI-84 (4-5#85) Estimating Average Sales with t he TI-84 and the Mean Value Theorem for Integrals (4-5#85)
Is the Alternating Series Remainder Theorem Not Working?
December 29, 2020 17:00 VideoThis appears to be a counter example that would disprove the Alternating Series Remainder Theorem....
A u-Substitution Using the Same U Formula Two Ways (4.5 p. 306 #57)
December 09, 2020 17:42 VideoA u-Substitution Using the Same U Formula Two Ways (4.5 p. 306 #57)
Using the TI-84 to Explore Some Accumulator Functions (4-5 p 307 #87)
December 08, 2020 05:33 VideoUsing the TI-84 to Explore Some Accumulator Functions (4-5 p 307 #87) The Calculator can compute the area between the x-axis and the blue function using brute force. We notice some relationships between them and spot points of inflection and extrema.
A Definite Integral with u-Substitution (4-5 p 305 #61)
December 08, 2020 04:50 VideoA Definite Integral with u-Substitution (4-5 p 305 #61). This one has a surprising result!
Some Complicated Integrals That Are Easier than they Appear! (4-5 p 307 #81)
December 08, 2020 04:32 Video4-5 p 307 #81 Some Complicated Integrals That Are Easier than they Appear! 4-5 p 307 #81 Some Complicated Integrals That Are Easier than they Appear! U-substitution to the rescue!
Using the Chain Rule with an Accumulator Function (4-4 p294 #83, 85)
December 08, 2020 03:53 VideoUsing the Chain Rule with an Accumulator Function (4-4 p294 #83, 85) If the derivative of the upper limit has a derivative more complicated than 1, then your better use the chain rule!