Derivatives
What does the derivative give us?
What is slope?
What does integration help you find?
Area, Volume, Critical Points
What is an Increase in Rate of Change?
Acceleration
Define Limits
What is, as x approaches a number, what is f(x) approaching.
what is a solid of revolution ?
It a solid obtained by rotating a plane figure around some straight line
y = 3x^2
y = 6x
5x^3/3-4x^2+5x+C
What is the extent of a two-dimensional surface withing a boundary?
Area
Lim(x)2
x->3
9d
lim ((x+a)1/2-x1/2)/a
a-->0
1/(2x1/2)
y = (x + 2)2 - 5x3
y = -15x2 + 2x + 4
Integration of (x^3/2+2x+3)dx
2x^5/2 /5+x^2+3x+C
What is a real number regardless of its sign?
Absolute value
Lim(x-7)2
x->-2
81
find dy/dx
xy+x2=4y3
(y+2x)/(12y2-x)
What is the difference between derivatives and integration?
Integration is the opposite process of doing the derivatives.
Integration of (1+3t)t^2 dt
t^3 /3+3t^4 /4+C
What is a process that maximizes or minimizes a quantity?
Optimization
Lim(1+1/x)x
x->infinity
e
(log20(25))(log5(20))
2
What is the purpose of a derivative?
The derivative can be used to find the equation of a tangent line to a graph at a particular point
Integration of (8/x-5/x^2+6/x^3)dx
What is a line that touches a curve at a point without crossing the line?
Tangent Line
Lim(sin(x)/x)
x->0
1
Intergration of (tanx/secx)2+(cotx/cscx)2 on [-100;100]
200