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Calculus 4E-Ch 8 & 9

Calculus 4E-Ch8:The Limit, Ch9:Method of Approximation&DefiningInstant.Speed

QuestionAnswer
Dividing by zero gives us an ________________ value in mathematics and is considered ______________________. undefined; forbidden
The LIMIT of a function is the value you approach but never ______________. reach
The PARADOX of speed is that speed is clearly a _______________ reality but seems __________________ incoherent. physical; mathematically
According to convention, the ____________ of the function f (x) is x and the ____________ is f(x) (or sometimes y). input; output
A value is forbidden for a specific function when it makes the denominator equal to ______________. zero
Write the formula equivalent of this statement: "1 is the limit of the function f(x) as x approaches 0." ____________________________
We would say x ≠ 0 beside a DERIVED/simplified function when 0 was the forbidden x-value from the ORIGINAL formula for the function (PRIOR to it being simplified).
A function ________ have a limit and a value at the SAME point SIMULTANEOUSLY. can
The 3 main concepts of calculus which are tied together by the Fundamental Theorem of Calculus are: 1) the limit of a function; 2) the derivative of a function; 3) the integral of a function
The ___________ is the most important of the 3 concepts of calculus because the other two are defined in terms of it. limit
Calculus helps us understand Western ____________________ history. intellectual
The ancient problem of change asks why there is both change and ____________ in the world. order
It is easy to determine the instantaneous speed of an object when the speed is ______________, but most speed is NOT constant. constant
the formula for average speed v(ave) = Δd/Δt
Acceleration means that speed is not constant, that speed IS _____________________. changing
Using the METHOD of APPROXIMATION, we find the instantaneous speed at some particular instant by calculating the AVERAGE speed over SMALLER and SMALLER time intervals near the particular instant. As the time interval approaches 0, the avg velocity approaches the instantaneous velocity for THAT particular instant.
In the METHOD of APPROXIMATION, we can make the time interval as ____________ as we want, depending on how accurate we want to be. small
In the METHOD of APPROXIMATION, we calculate the average speed for multiple time intervals so that we can see the metaphorical "path" that the average speed is taking as it approaches the instantaneous speed.
As Δt approaches 0, the average velocity approaches the ____________________ velocity. instantaneous
Instantaneous velocity is the LIMIT of the average velocity as Δt approaches _____. 0
Created by: MrsHough
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