Calculus (Basic Ideas and Limits) Flashcards
Calculus Meaning
In Latin
small stone / pebble
Calculus
Mathmatical study of change, focuses on instant rate of change and accumulation
Two main types of Calc
Differential Calculus
Integral Calculus
Differential Calc
instantaneous rates of change
involves process of differentiation or determining derivates including a limit
Integral Calc / Antiderivative
accumulation of areas or areas of irregular shapes / process of integration or determining the anti-derivatives or evaluating definite integrals involving a limit
Fundmental Principal
You can use approximations of increasing accuracy to find an exact answer
Differential Calc
Secant Line
What is the formula for the average rate of change?
Straight Line that intersects a curve in 2 points
Slope of the Secant Line : m= (y2-y1)/(x2-x1)
Differential Calc
Tangent Line
Straight Line that just touches a curve at a single point
The slope of the tangent line and function at that point are equal
Instantaneous rate of change = slope of tangent line
Differential Calc
Secant Line —> Tangent Line
Not a question just a note
As the 2 points on the secant line gets closer to the point “x” the slope of the secant line approches the slope of the tangent line (As Δx -> 0)
Ingeral Calc
No question, just note
When finding the area under the line, the more retangles the closer you get to the actual area
Limits
lim_x->c f(x) = L
x->c within this interval f(x) is aproching L
As x approches c, the limit of f(x) is L if all values of f(x) are close to L for all walues of x are close but not equal to c
Where is the limit approching from?
lim f(x)=L
as x –> c^-
Limit from left ie values less than c
Where is the limit approching from?
lim f(x)=L
as x –> c^+
limits from right ie values greater than c
IF lim_x->1^+ = -2 AND lim_x->1^- = 3
THEN lim_x->1= WHAT
DNE
