Write Claim As a Limit

[nycmathdad]

Professor Smith claims that a student’s final exam score is a function of the time t (in hours) that the student studies. He claims that the closer to
seven hours one studies, the closer to 100% the student scores on the final. He claims that studying significantly less than seven hours may cause one to be underprepared for the test, while studying significantly more than seven hours may cause
“burnout.” Write Professor Smith’s claim symbolically as a limit.

Let me see.

A function of the time t = f(t).

Closer to 7 hours = t tends to 7.

I say the limit = 100 percent

My answer is:

lim f(t) = 100
t--> 7

Is this right?

 

[jonah2.0]

Beer soaked recall follows.

Professor ...

Repost from

Write Claim As a Limit

Professor Smith claims that a student’s final exam score is a function of the time t (in hours) that the student studies. He claims that the closer to seven hours one studies, the closer to 100% the student scores on the final. He claims that studying significantly less than seven hours may...

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[Dr.Peterson]

Professor Smith claims that a student’s final exam score is a function of the time t (in hours) that the student studies. He claims that the closer to seven hours one studies, the closer to 100% the student scores on the final. He claims that studying significantly less than seven hours may cause one to be underprepared for the test, while studying significantly more than seven hours may cause “burnout.” Write Professor Smith’s claim symbolically as a limit.

Let me see.

A function of the time t = f(t).

Closer to 7 hours = t tends to 7.

I say the limit = 100 percent

My answer is:

lim f(t) = 100
t--> 7

Is this right?

I'm sure that's what was intended by the problem. But the claim in the problem really doesn't imply that!

What it does say is that f(t) increases monotonically for t less than 7, and decreases monotonically for t greater than 7; but it doesn't imply that you can get as close to 100% as you wish by approaching 7 hours from above or below, which is what a limit means. The function might, for example, be f(t) = 90 - 10|t-7|.

But that's just being picky. (Math is all about pickiness; teaching math isn't. I'm guessing that the author of this problem was not functioning as a mathematician.)

 

[nycmathdad]

I'm sure that's what was intended by the problem. But the claim in the problem really doesn't imply that!

What it does say is that f(t) increases monotonically for t less than 7, and decreases monotonically for t greater than 7; but it doesn't imply that you can get as close to 100% as you wish by approaching 7 hours from above or below, which is what a limit means. The function might, for example, be f(t) = 90 - 10|t-7|.

But that's just being picky. (Math is all about pickiness; teaching math isn't. I'm guessing that the author of this problem was not functioning as a mathematician.)

Is my answer correct? I like your function but what about the limit as x tends to 7 for f(t) = 100?

 

[jonah2.0]

Beer soaked ramblings follow.

Is my answer correct? I like your function but what about the limit as x tends to 7 for f(t) = 100?

It's an odd numbered exercise.
You can easily verify that by going to that section of your book that says Answers To Odd Numbered Exercises.

 

[Dr.Peterson]

Is my answer correct? I like your function but what about the limit as x tends to 7 for f(t) = 100?

I said:

I'm sure that's what was intended by the problem. ...

Isn't that clear enough? Yes, it's "correct". It's the problem that is wrong.

After answering you, I made what amounts to a negative comment about the book (but, really, it's about the general tendency of textbooks, in the name of relevance, to make problems that confuse really thoughtful people). You were intended to ignore that part, which was directed at others who might be interested.

 

[nycmathdad]

I said:

Isn't that clear enough? Yes, it's "correct". It's the problem that is wrong.

After answering you, I made what amounts to a negative comment about the book (but, really, it's about the general tendency of textbooks, in the name of relevance, to make problems that confuse really thoughtful people). You were intended to ignore that part, which was directed at others who might be interested.

I like the way you think. I like your replies. Look for my new thread entitled HOW MANY MATH QUESTIONS IS ENOUGH? I need an honest, professional reply.

 

[jonah2.0]

Beer soaked ramblings follow.

I like the way you think. I like your replies. Look for my new thread entitled HOW MANY MATH QUESTIONS IS ENOUGH? I need an honest, professional reply.

This from someone who once answered Dr.Peterson sarcastically with

I help FOR FREE all the time. It depends on financial status. Living CHECK TO CHECK is very difficult. Know what I mean, professor?