Monday, January 11, 2021

A Tangent Line Confirmed with the TI-84 (5-1 p322 #69)

 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)

 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)

 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 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)

 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)

 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)

 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.

Sunday, January 10, 2021

Mean Value Theorem for Integrals with the TI-84 (4-5#85)

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)

Tuesday, December 29, 2020

Is the Alternating Series Remainder Theorem Not Working?

 



This appears to be a counter example that would disprove the Alternating Series Remainder Theorem.... 

Monday, December 7, 2020

Using the TI-84 to Explore Some Accumulator Functions (4-5 p 307 #87)

 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 extrema. 

A Definite Integral with u-Substitution (4-5 p 305 #61)

A 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)

 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)

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!

An Accumulaotr function without a constant 4-4 (p. 294 #81)

 

An Accumulaotr function without a constant 4-4 (p. 294 #81)


Without one of the limits being a constant, you can't use the 2nd FTC... what to do?  Invent one!

An Accumulation function (4.4 p. 293# 67)

An Accumulation function (4.4 p. 293# 67)



 An Accumulation function is a function that is a function of the accumulation of area under a curve.  A nice feature is that the derivative is based on the integrand itself


Another Slope Field and Differential Equation with Natural Logs (5-2 p330 #50)

 Another  Slope Field and Differential Equation with Natural Logs (5-2 p330 #50)