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#1 2012-04-22 20:10:44

mukesh
Member
Registered: 2010-07-18
Posts: 31

ranfe of function

find the range of function
1)f(x)=sinx+cosx+3
2)f(X)=\x-1\ +\x-2\+\x-3\

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#2 2012-04-22 20:14:17

Bob
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Registered: 2010-06-20
Posts: 10,053

Re: ranfe of function

hi mukesh,

Answer coming up, so stay on-line.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2012-04-22 20:14:47

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: ranfe of function

Hi mukesh

Let's do the first one together.Do you know any formulas for converting the sum of a sin(x) and a cos(x) to a product?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#4 2012-04-22 20:17:18

Bob
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Registered: 2010-06-20
Posts: 10,053

Re: ranfe of function

Q1.  So what's the biggest this could be?  sin x and cos x could each be 1, but not at the same time.

This will have a maximum when tanx = 1, so the maximum for Q1 is root 2 + 3

Similarly the minimum will be when tan x = -1 giving a minimum of 3 - root 2.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#5 2012-04-22 20:22:27

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: ranfe of function

Q2.

I'm assuming those \  \ lines are for 'absolute values'

As x tends to infinity all three absolutes tend to infinity too.

Now, what's the smallest those three bits could be?

Try some critical values.

x = 0

expression = 1 + 2 + 3 = 6

x = 1

expression = 0 + 1 + 2 = 3

x = 2

expression = 1 + 0 + 1 = 2

x = 3

expression = 2 + 1 + 0 = 3

The graph is symmetrical about x = 2 so that's the minimum.

So the range is [2, ∞)

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#6 2012-04-22 20:31:44

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: ranfe of function

Here is another way for the first question:

Notice that:

Because the minimum of the sin(x) function is -1 and the maximum is 1,the minimum and maximum of the function

will be -√2 and √2,so when we add the 3 on top we get that the minimum and maximum of your first function are:

Last edited by anonimnystefy (2012-04-22 20:31:57)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#7 2012-04-22 20:42:31

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: ranfe of function

And here is the graph Bob was talking about:

gif&s=39&w=290&h=136&cdf=RangeControl

gif&s=39&w=313&h=135&cdf=RangeControl

Last edited by anonimnystefy (2012-04-22 22:27:33)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#8 2012-04-22 22:01:48

mukesh
Member
Registered: 2010-07-18
Posts: 31

Re: ranfe of function

thanks from the heart

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#9 2012-04-22 22:02:41

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: ranfe of function

You are welcome.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#10 2012-04-22 22:24:10

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: ranfe of function

hi mukesh and Stefy,

Sorry, I had to rush away quickly.

Thanks, Stefy for filling in the gaps.  Your Wolfram graph images are not showing for me.

So I've made the three absolutes separately using Sketchpad, and then the combined graph using


http://www.mathsisfun.com/data/function … =-8&ymax=8

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#11 2012-04-22 22:25:14

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: ranfe of function

Hi bob

Wolfram's graphs seem to have unstable links or something.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#12 2012-04-22 22:29:20

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: ranfe of function

Does it show for you?

Maybe there's part of it only on your machine.  So the rest of us cannot view it.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#13 2012-04-22 22:31:19

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: ranfe of function

I don't know.After some time it doesn't show me either.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#14 2012-04-23 05:19:29

juantheron
Member
Registered: 2011-10-19
Posts: 312

Re: ranfe of function

(2) Let

Using Triangle Inequality

Where

So

equality hold when

So

So

at

So

Last edited by juantheron (2012-04-23 05:24:17)

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