Find limit of the function without l’hospital’s rule

[Kholostovamk]

I need to find a limit x->0 in function
( sqrt(x+5) - sqrt(5))/x
Without using derivative
Need solution, not the answer
Pls

 

[Deleted member 4993]

I need to find a limit x->0 in function
( sqrt(x+5) - sqrt(5))/x
Without using derivative
Need solution, not the answer
Pls

Have you studied Taylor's series expansion?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[pka]

I need to find a limit x->0 in function
( sqrt(x+5) - sqrt(5))/x
Without using derivative
Need solution, not the answer

[imath]\dfrac{{\sqrt {x + 5} - \sqrt 5 }}{x} = \dfrac{1}{{\left( {\sqrt {x + 5} + \sqrt 5 } \right)}}[/imath]

[imath][/imath][imath][/imath]

 

[Kholostovamk]

Have you studied Taylor's series expansion?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

We didn’t go through Taylor’s expansion yet, so I was told by professor that we need to find it with other way
Like factoring, regrouping etc

 

[Deleted member 4993]

We didn’t go through Taylor’s expansion yet, so I was told by professor that we need to find it with other way
Like factoring, regrouping etc

Look at response #3

 

[Kholostovamk]

[imath]\dfrac{{\sqrt {x + 5} - \sqrt 5 }}{x} = \dfrac{1}{{\left( {\sqrt {x + 5} + \sqrt 5 } \right)}}[/imath]

[imath][/imath][imath][/imath]

[imath]\dfrac{{\sqrt {x + 5} - \sqrt 5 }}{x} = \dfrac{1}{{\left( {\sqrt {x + 5} + \sqrt 5 } \right)}}[/imath]

[imath][/imath][imath][/imath]

It doesn’t make sense, how the first part became second
And it doesn’t look like limit
Sorry I don’t understand

 

[Dr.Peterson]

I need to find a limit x->0 in function
( sqrt(x+5) - sqrt(5))/x
Without using derivative
Need solution, not the answer
Pls

Key idea: Use the conjugate. (Rationalize the numerator.)

 

[pka]

It doesn’t make sense, how the first part became second
And it doesn’t look like limit
Sorry I don’t understand

You need to take a refresher course in basic precalculus.
[imath]\dfrac{\sqrt{x+5}-\sqrt{5}}{x}\left(\dfrac{\sqrt{x+5}+\sqrt{5}}{\sqrt{x+5}+\sqrt{5}}\right)=\dfrac{\cancel{x}}{\cancel{x}(\sqrt{x+5}+\sqrt{5})}[/imath]

 

[Deleted member 4993]

It doesn’t make sense, how the first part became second
And it doesn’t look like limit
Sorry I don’t understand

It does not make sense because I suspect that you are not using pencil & paper. You are probably just staring at the screen.

In addition, you need to review algebra. Without mastering Algebra, Calculus will be an insurmountable mountain.