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A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500...

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Math 165 SI

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Page 1: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

Math 165 SI

Page 2: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

CalculusA.R.C./I.R.C./

ContinuityTrig LimitsLimits

Definitions/Facts

500

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400

500

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500

Page 3: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

What is the average rate of change

Page 4: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

if when substituting values in for x very close to c it approaches L and no other number

What is the definition of a limit

Page 5: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

What is the Instantaneous Rate of Change

Page 6: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

When you can trace you finger cross the graph of a function without picking it up

What is a continuous function?

Page 7: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

1. Jump discontinuity2. The function grows too large

3. Oscillates, does not settle in on a single number

What are the three ways a limit fails to exist ?

Page 8: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

)

6

Page 9: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

)

1/2

Page 10: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

)

-1

Page 11: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

)

75

Page 12: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

)

12

Page 13: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

)

0

Page 14: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

)

4

Page 15: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

)

4

Page 16: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

)

0

Page 17: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

)

3

Page 18: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

Find A.R.C. of cot(x) on the interval [π/4, 3π/4]

-π/4

Page 19: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

Determine the Intervals on which the function ((3x^2-x-2)/(x-1))is continuous

(-,1),(1,

Page 20: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

Find an equation for the tangent line of x^3-12x at the point (1, -11)

y=-9x-2

Page 21: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

For what value of a is f(x)= continuous at every x

4/3

Page 22: A.R.C./I.R.C. /Continuity Trig Limits Limits Definitions/ Facts 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

For what value of a and b is f(x)= continuous at every x

A=5/2, b=-1/2

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