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

## Wednesday, January 20, 2021

### Slope Fields and Differential Equations with Natural Logs (5-2 p330 #49)

Slope Fields and Differential Equations with Natural Logs (5-2 p330 #49)

A slope field and a diffyQ checked with the TI-84

## Tuesday, January 19, 2021

### Long Division Before Integrating (5-2 p330 #17)

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!

## 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)

### 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....

## Wednesday, December 9, 2020

## 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.

### 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)