query 11

course Mth 271

i dont know how to graph the piecewise functions or the greatest integer functions.

l??C????>???x??assignment #011

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011. `query 11

Applied Calculus I

10-13-2007

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15:43:51

1.6.16 (was 1.6.14 intervals of cont for (x-3)/(x^2-9)

What are the intervals of continuity for the given function?

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RESPONSE -->

this is actually ? 18 which wasnt assigned but...

x cannot equal -3 or 3, since this would result in division by zero so

(neg infin, -3) (-3,3) (3, pos infin)

confidence assessment: 3

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15:44:49

The function is undefined where x^2 - 9 = 0, since division by zero is undefined.

x^2 - 9 = 0 when x^2 = 9, i.e., when x = +-3.

So the function is continuous on the intervals (-infinity, -3), (-3, 3) and (3, infinity).

The expression (x - 3) / (x^2 - 9) can be simplified. Factoring the denominator we get

(x - 3) / [ (x - 3) ( x + 3) ] = 1 / (x + 3).

This 'removes' the discontinuity at x = +3. However in the given fom (x-3) / (x^2 + 9) there is a discontinuity at x = -3. **

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RESPONSE -->

yup

self critique assessment: 3

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15:46:50

1.6.24 (was 1.6.22 intervals of cont for |x-2|+3, x<0; x+5, x>=0

What are the intervals of continuity for the given function?

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RESPONSE -->

this problem isnt in the book, and i dont know how to graph piecewise functions on my calculator

confidence assessment: 0

You shouldn't be using a calculator to construct your graphs; you should construct them using your knowledge of the functions.

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15:50:54

The graph of y = |x-2|+3 is translated 2 units in the x direction and 3 in the y direction from the graph of y = |x|. It forms a V with vertex at (2, 3).

The given function follows this graph up to x = 0. It has slope -1 and y-intercept at y = | 0 - 2 | + 3 = 5.

The graph then follows y = x + 5 for all positive x. y = x + 5 has y-intercept at y = 5. From that point the graph increases along a straight line with slope 1.

So the graph of the given function also forms a V with vertex at (0, 5).

Both functions are continuous up to that point, and both continuously approach that point. So the function is everywhere continuous. **

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RESPONSE -->

you know i havent seen piecewise functions in about 6 years

self critique assessment: 0

There's apparently a mixup between the query and the text. However you should be sure you understand the given solution.

You should know the graph of y = | x | and how to use translations to get the graph of y = | x - 2 |, as in the first sentence.

The graph follows this function up to x = 0, at which point its y value is 5. As you approach x = 0 along this graph, the limiting value of y is 5.

Then it begins following the function y = x + 5. If you approach x = 0 along this line the limiting value of y = 0 + 5 = 0.

Since the limiting value at x = 0 is the same from both directions, the function is continuous at that point.

Be sure you understand this.

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15:52:06

1.6.66 (was 1.6.54 lin model of revenue for franchise

Is your model continuous? Is actual revenue continuous?

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RESPONSE -->

this ? wasnt assigned

revenue should be continuous as long as you're making money

confidence assessment: 0

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15:53:11

revenue comes in 'chunks'; everytime someone pays. So the actual revenue 'jumps' with every payment and isn't continuous. However for a franchise the jumps are small compared to the total revenue and occur often so that a continuous model isn't inappropriate for most purposes. **

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RESPONSE -->

that doesnt make sense. revenue would be an exponential function as long as you're making money, which should be a continuous graph.

self critique assessment: 1

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15:53:23

Add comments on any surprises or insights you experienced as a result of this assignment.

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...

self critique assessment: 3

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"

See my note on the piecewise function and be sure you understand. If not, let me know what you do and do not understand.