Limits Flashcards
1
Q
lim x->0 sin(x)/x
A
1
2
Q
lim x->0 1-cos(x)/x
A
0
3
Q
A tangent line is…
A
A line through a point on a curve with a slope equal to the slope of the curve at that point
4
Q
A secant line is…
A
The line connecting two points on a curve
5
Q
A normal line is…
A
The line perpendicular to the tangent line at the point of tangency
6
Q
f(x) is continuous at x = c when…
A
f(c) exists
lim x->c exists
lim x->c f(x) = f(c)
7
Q
f ’(x) = … (or difference quotient)
A
lim h->0 (f(x+h) - (fx))/h
8
Q
f ‘(c) =…
A
lim x->c (f(x) - f(c))/x - c
9
Q
What does f ‘(x) tell you about a function
A
Slope of curve at one point
Slope of the tangent line
Instantaneous rate of change
10
Q
Average rate of change is…
A
delta-y/delta-x = (f(b) - f(a))/b - a
