Thursday, September 10, 2020

Intro to Derivatives

 


Introducing the idea that a slope of a curve depends on the value of x... so we call the slope formula a derivative... The limit of the slope of a secant line is how we get this major topic started!

Wednesday, September 9, 2020

Some Ch P and Chapter 1 Review Questions




 A few problems are explained, including tangent lines, and the Intermediate Value Theorem (IVT).

The arc length of a predator chasing prey

 Using the arc length integral we can show that a predator can travel twice the distance in the same amount of time!



Monday, September 7, 2020

Derivatives of Common Functions Review

 


A review of the derivatives of the basic functions, with a derivation of a few of them.

Answer it yourself before you watch.

Saturday, September 5, 2020

One Sided, "Type 2" Limits

 

Type 2 limits are the type that when you substitute the number that x is going towards, you get a fraction with a number in the numerator and a 0 in the denominator (->L/0).  The division by zero is associated with a vertical asymptote, so the limit will go to either positive infinity or negative infinity.

Continuity and the IVT (1.4, #63, 83, 85)

 


Using the requirements of Continuity, we can find a way to make a piece wise function continuous.  We also look at using the Intermediate Value Theorem (IVT) to prove the existence of a zero of a function on a certain closed interval.

Arc Length (7.4 #11)

An exact length of arc can be computed with the arc length formula, together with a bit of algebra, so the integrand is a product of factors where one factor is the derivative of the other so we can use "U-substition"

Intro to Derivatives

  Introducing the idea that a slope of a curve depends on the value of x... so we call the slope formula a derivative... The limit of the sl...