Chapter 2 Flashcards

(15 cards)

1
Q

Slope-Intercept Form

A

y = mx + b

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2
Q

Slope (m)

A

Rise / Run

y2-y1/x2-x1

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3
Q

Point-Slope Form

A

y - y1 = m(x-x1)

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4
Q

What happens to the slope of the secant line as b approaches a?

A

It approaches the slope of the tangent line

msec –> mtan

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5
Q

What is a secant line?

A

A straight line joining two points on a function.

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6
Q

What does the secant line represent?

A

The average rate of change of a function between two points.

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7
Q

Average Velocity =

A

Total Distance / Total Time

Change in distance over time

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8
Q

Instantaneous Velocity

A

Velocity at a specific time

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9
Q

Definition of a Limit

A

Suppose f(x) is defined when x is near the number a (This means that f is defined on some open interval that contains a, except possibly a itself.)

The limit of f(x), as x approaches a equals L if we can make the value of f(x) arbitrarily close to L by taking x to be sufficiently close to a (on either side of a) but not equal to a

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10
Q

Basic Limit Formula

A
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11
Q

What are the two ways to estimate a limit?

A
  1. Evaluate f(x) at points near a.
  2. Trace the graph and see y values
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12
Q

When are cases when a limit does not exist?

A
  1. Oscillating functions
  2. When the value of L is different on two sides

L is a unique value

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13
Q

Definition of a Left-Handed Limit

A

The left-handed limit of f(x) as x approaches a (or the limit of f(x) as x approxhes a from the left) is equal to L if we can make the values of f(x) arbitrarily close to L by taking x to be sufficiently close to a and x less than a.

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14
Q

Definition of a Right-Sided Limit

A

The right-hand limit of f(x) as x approxhes a (or the limit of f(x) as x approaches a from the right) is equal to L if we can make the values of f(x) arbitrarily close to L by taking x to be sufficiently close to a and x greater than a.

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15
Q

Limit Theorem

A
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