Homework # 3 Due: 6/6/06 1. Find an equation of the tangent line to y = 2x + 1 at the point (4,3).
2. Draw a graph of a function f that has the properties g(0) = 0 g (0) = 3 g (1) = 0 g (2) = 1 3. U
Homework # 1 Due: 05/23/06 #1 Find the domain of the following functions 3x2 - 2x + 1 a) f (x) = 2 x - 4x - 21 3 b) f (x) = x + 3 - x - 2 + x2 - 1 1 c) f (x) = x2 - 1 #2 Graph the following piecew
Quiz # 1 Name: 1. Find f (2 + h), f (x + h), and f (x + h) - f (x) if f (x) = x - x2 . h
2. Classify each function as a power function, root function, polynomial (state its degree), rational function
Homework # 3 Due: 6/6/06 1. Find an equation of the tangent line to y = 2x + 1 at the point (4,3).
The equation of a tangent line to y = f (x) at (a, b) is (y - b) = f (a)(x - a). First, we 1 write
1
Tangents and Velocities
Recall finding tangents numerically.
1.1
Tangents
Remember formula for slope of secant line. Definition 1. The tangent line to the curve y = f (x) at the point (a, f (a)
1
Maximum and Minimum Values
This is all about optimization problems. Definition 1. A function f has an absolute maximum at c if f (c) f (x) for x in the domain of f . f (c) is called the maximum v
Homework # 6 Due: Never
1
New Material
1. Use the guidelines of this section to sketch the curve. (a) f (x) = 20x3 - 3x4 (b) f (x) =
x2 x2 -9
(c) f (x) = sin x 2. If 1200 cm2 is available to make a
Homework # 6 Due: Never
1
New Material
1. Use the guidelines of this section to sketch the curve. (a) f (x) = 20x3 - 3x4 i. Domain f is a polynomial, so its domain is all real numbers. ii. Intercept
Homework # 4 Due: 6/13/06 1. Differentiate the following: (a) f (x) = x2 (cos x)(sin x) (b) f (x) = (c) f () = (d) f (x) =
tan x-1 sec x sin (+tan ) 1+sec (x-1)4 (x2 +2x)5
(e) f (x) = sin tan
sin
Homework # 2 Due: 5/30/06 1. Use the graph to find the following limits: lim f (x) lim f (x) lim f (x) lim f (x) lim f (x)
x2+ x0
x2-
x2
x-1
2. Sketch the graph of a function that satisfies all o
Homework # 1 Due: 05/23/06 #1 Find the domain of the following functions 3x2 - 2x + 1 a) f (x) = 2 x - 4x - 21 The domains of 3x2 - 2x + 1 and x2 - 4x - 21 are all real numbers. So the domain of f is
Homework # 2 Due: 5/30/06 1. Use the graph to find the following limits: lim f (x) lim f (x) lim f (x) lim f (x) lim f (x)
x2+ x0
x2-
x2
x-1
2. Sketch the graph of a function that satisfies all o
1
Related Rates
So far we've been looking at the rate of change of one "thing". Maybe it's a particle or just a function or what have you. A lot of the time, however, when something changes it cause
1
Formulas
Remember, mathematics is all about being lazy. Using the limit definition of the derivative will get very difficult if we have to do it every time. Fortunately, we have methods for comput
1
1.1
Continuity
Definitions
Last time, I went over the direct substitution property. That says that for polynomials and rational functions, as long as a is in the domain, lim f (x) = f (a). It turn
1
Tangents and velocities
On the first day, I talked very briefly about where calculus comes from. One branch comes from studying tangent lines to curves. Here's a more in-depth overview. A tangent
1
1.1
Trigonometry
Angles
I mentioned on Tuesday that we don't use degrees in calculus. Instead we use a unit called radians. Definition 1. One radian is the angle that gives an arc length equal to
1
1.1
Functions
What is a function?
All a function is, is something that takes a number and turns it into another number. Example 1.1. Remember from geometry class the formula for a circle, A = r2 .