Tangent Line
Mr. Koster
General Calculus
Limits
Limits of Trig Functions
100

Use the limit process to find the slope of the graph of the function at the specified point. g(x) = 4/x,    (2,2)

-1

100

The name of Mr. Koster's dog.

Valentino

100
Name three times when a limit does not exist.
1. f(x) approaches a different number from left and right side of c 2. f(x) increases or decreases without bound 3. f(x) oscillates between two fixed values
100
lim┬(x→-1)⁡ (x^2-1)/(x+1)
-2
100
lim┬(x→0) ⁡cos⁡x
1
200

________ is the study of the rates of change of functions.Number of radians for a complete circle

Calculus

200

Mr. Koster's favorite holiday season.

Halloween

200
Name the three parts of calculus.
Limits Differentiation Integration
200
lim┬(x→-3)⁡ (x^2+x-6)/(x^2-9)
5/6
200
lim┬(x→0)⁡ sin⁡3x/2x
3/2
300

a)  Find a formula for the slope of the graph. b)  Use the formula to find the slope at the given point. g(x) = 1/(x+4),     (-2, 0.5)

a)  -1/(x+4)^2 b)  -1/4

300

Where Mr. Koster lives.

Orlando, Florida

300
What does the notation lim x->8 f(x) = 25 mean?
As x gets arbitrarily close to 8, f(x) approaches 25
300
lim┬(x→2) ⁡3/(4x)
3/8
300
lim┬(x→0)⁡ (cos⁡ x tan ⁡x)/x
1
400

a)  Find the slope of the graph of f at the given point. b)  Use the result to find an equation of the tangent line to the graph at the given point. f(x) = x^2 - 1,     (2, 3)

a)  4 b)  y = 4x-5

400

The college where Mr. Koster earned his bachelor's degree.

Ohio University

400
If f(2)=4, can you conclude anything about the limit of f(x) as x approaches 2?
No
400
lim┬(x→3)⁡〖(√(x+1)-2)/(x-3)〗
1/4
400
lim┬(x→π)⁡ x sec⁡x
-Pi
500

What is the linear equation written in point-slope form.

y-y1 = m(x - x1)

500

Where Mr. Koster works part time in entertainment production management.

Universal Studios

500

If the limit of f(x) as x approaches 2 is 4, can you conclude anything about f(2)?

No

500
lim┬(x→4)⁡〖(x^2-5x+4)/(x^2-2x-8)〗
1/2
500

lim┬(x→0)⁡ (1-cos⁡ x)/x

0

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