By Chris Thiel
Calculus and other math problems explained
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Not 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 Before Calculus you used Algebra to solve for x. Now in Calculus we use Algebra to manipulate an expression to make for easy Calculus!
How 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"...
An 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 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 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...
Related Rates Example Problems Here are 7 examples of Related Rates problems.
Using L'Hôpital's Rule on an e^x Function
Inverse Functions Have Reciprocal Slopes (5.R p 400 #39)
A u-sub for arctan (5-R p. 400 #109)
A Hybrid Parametric Area with d(theta) (10-R p.747 #57)
Elliptical 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...
Definite Integral with arcsine (5.8 p387 #33)
Finding a Tangent Line Implicitly on a function with e^x (5.4 p348 #65)
Implicit Differentiation with e^x (5.4 p 348 #63)
Verifying a Differential Equation involoving e^x (5.4 p349 #69)
A 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) This includes u-substitution, and an exponential function in base 2
Derivative 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) 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) 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)
The 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)
Limiting the Domain of a Absolute Value Function so it would have an inverse (5.3 p340 #57)
Inverse 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)
Review of a Midpoint Riemann Sum (5.2 p 331 #77)
The Area of a Region That Involves a Secant Function (5.2 p331 #71)
Another Definite Integral without u-Substitution (5.2 p 331 #65)
A Definite Integral Requiring u-Substitution (5.2 p 330 #51)
Another Slope Field and Differential Equation with Natural Logs (5-2 p330 #50)
Slope 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)
Long Division AND u-Substitution help this Integral (5-2 p330 #21)
Long 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)
A 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) We use the quotient rule together in this example.
U-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...
Using 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) 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) 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) Estimating Average Sales with t he TI-84 and the Mean Value Theorem for Integrals (4-5#85)
This 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)
Using 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...
A Definite Integral with u-Substitution (4-5 p 305 #61). This one has a surprising result!
4-5 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) If the derivative of the upper limit has a derivative more complicated than 1, then your better use the chain rule!
