AP Calculus

Blog Notes:

Review of homework:
Derivative is the instantaneous rate of change. Geometrically represents the slope of the tangent line.

Limit: (technical definition)
L is the limit of f(x) as x approaches c
If and only if
L is the number you can keep f(x) arbitrarily close to just by keeping X close enough to C, but not equal to C.

Basically, if you can keep X close to any X value (C) and your Y value stays relatively the same, then the Y value is the limit.

For the function f(x)=x^2, say that your C value is 2. So your X is approaching 2, but never quite getting there. The question is, does your Y value stay around 4 (f(2)=2^2=4)? If it does, than 4 is the limit of this function. In this case, 4 is the limit because when X is around 2, Y equals around 4.

Definite Integral:
The product of X and Y, which is also the area underneath the curve.

(An example of the area underneath the curve between x=a and x=b. Also known as the definite integral.)

The definite integral is not just a number, it has meaningful units. If your graph is one of velocity over time, for example (velocity as the Y-axis and time as the X-axis), then your definite integral has a value of distance. This is because when you multiply , Time cancels and you’re left with only distance.

Quiz:
Instantaneous rate of change
Increasing or decreasing functions
Trig values
Definitions of derivative and limit
Possible problems from last week’s quiz

Homework: page 16 all Quickies
#’s 1, 3, 6, 9

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