Math Is Fun Forum

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Limits of x+sqrt(x^2+2x)

As text book suggested in one of the examples, I tried to multiply by conjugate radical:

After a few iterations I came up with

Which does not lead me anywhere....
So I am starting to think that multiplication by conjugate radical is not a way to go.
But what is the way to go???

By graphing the function I see that

But I have no idea how to prove it.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits of x+sqrt(x^2+2x)

Hi;

Use for the denominator the relationship,

when x < 0.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: Limits of x+sqrt(x^2+2x)

Ok... but how this will help?

Or did I make a mistake somewhere?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits of x+sqrt(x^2+2x)

Where are the other parts of the fraction?

---

“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.

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: Limits of x+sqrt(x^2+2x)

Where are the other parts of the fraction?

"other" parts?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits of x+sqrt(x^2+2x)

Hi White_Owl

Last edited by anonimnystefy (2012-06-17 03:37:42)

---

“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.

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: Limits of x+sqrt(x^2+2x)

Hi White_Owl

Ok... But if we continue from here:

????

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits of x+sqrt(x^2+2x)

Hi White_Owl;

Or did I make a mistake somewhere?

You forgot the numerator.

Starting from your limit in post #1.

Using the rather odd relationship from post#2 for the denominator.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits of x+sqrt(x^2+2x)

Hi;

Use for the denominator the relationship,

when x < 0.

How did you get the + sign?

---

“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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits of x+sqrt(x^2+2x)

Nevermind,I got it.

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits of x+sqrt(x^2+2x)

Hi;

Had it in my notes and it works for some reason. Putting a minus sign there does not.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits of x+sqrt(x^2+2x)

I figured it out:

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits of x+sqrt(x^2+2x)

For all x<0  the √x^2 = -x is how it is phrased over here.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits of x+sqrt(x^2+2x)

Did you see the post before yours?

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits of x+sqrt(x^2+2x)

Hi;

Yes, but I thought I already said that in post #2?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits of x+sqrt(x^2+2x)

I was just confirming that I understood it.

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits of x+sqrt(x^2+2x)

Hi;

I know that too.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits of x+sqrt(x^2+2x)

Why are we even discussing this, then?

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits of x+sqrt(x^2+2x)

Hmmm. I do not know the answer to that.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits of x+sqrt(x^2+2x)

Ok.

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits of x+sqrt(x^2+2x)

How did you do on your tests?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits of x+sqrt(x^2+2x)

Which test?

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits of x+sqrt(x^2+2x)

All of them. How did you do?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: Limits of x+sqrt(x^2+2x)

Wow!
Thank you, guys.
Sometimes you have to be creative to get an answer. And I always believed math is a precise science... I wonder why

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits of x+sqrt(x^2+2x)

I can'tremember all of them right now,but I will tell you that all of my final grades are good except Psychology (4) and Serbian (probably 3).

---

“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.