Day 7, Mat128: Calculus A

• You have a new assignment.

• We will have a quiz over section 1.3: the derivative at a point at the end of class.

Definition 1.4.2. Let $f$ be a function and $x$ a value in the function's domain. We define the derivative of f, a new function called $f^{\prime }$ by the formula $$f^{\prime }(x)=\underset{h\to 0}{lim}\frac{f(x+h)-f(x)}{h}$$ provided this limit exists.

• Let's take a look at a couple of the activities in section 1.4:
  • Activity 1.4.2: these are a little troublesome because we don't have scales for the "change in x" and the "change in y"....
    
    

  • 1.4.3 Exercises, #3 is along the same vein.

• Time for a worksheet.

• Then a quiz!

• I really like this exercise, referenced in the text. Fun and challenging!
• Limit laws you can believe in!