Seeking help for limit math problem

[teffy3001]

lim (sqrt(x^2+5) - 3)/(x-2)
x->2


i hope that kinda makes sense...

anyways, my question is that I've been doing this and i keep getting 0 in the denominator in the answer...after subsituting everything i got 4/ sqrt(9) - 3 = 4/0
so then is this equation just not possible?

 

[matt grime]

after subsituting everything i got 4/ sqrt(9) - 3 = 4/0

How did you get this? That doesn't appear to bear any relation to the initial expression you gave.

 

[Saladsamurai]

lim (sqrt(x^2+5) - 3)/(x-2)
x->2


i hope that kinda makes sense...

anyways, my question is that I've been doing this and i keep getting 0 in the denominator in the answer...after subsituting everything i got 4/ sqrt(9) - 3 = 4/0
so then is this equation just not possible?

For \lim_{x \rightarrow 2}\frac{\sqrt{x^2+5}-3}{x-2}

Clearly the substitution method will give you a zero denominator!

So, what methods have you learned to try and "avoid" a zero denominator?

Casey

How did you get this? That doesn't appear to bear any relation to the initial expression you gave.

I think they meant (sqrt(4+5)-3)/0...
Arithmetic errors are always a good start

 

[teffy3001]

um the course I am taking told me first multiply the numerator and denominator by
sqrt(x^2+5) - 3

i might have done it wrong but then i got x^2+5-9/x-2(sqrt(x^2+5) - 3)
i factored that to x^2-4/x-2(sqrt(x^2+5) - 3)
and then eventually got (x-2)(x+2)/x-2(sqrt(x^2+5) - 3)
canceled out x-2
x+2/sqrt(x^2 + 5) - 3
then subtituted the x for 2
thats how i got that answer...i think that's how the teacher told me to do it...probably made mistakes along the way though..im not sure

 

[EnumaElish]

um the course I am taking told me first multiply the numerator and denominator by
sqrt(x^2+5) - 3

i might have done it wrong but then i got x^2+5-9/x-2(sqrt(x^2+5) - 3)

Where is the interaction term in your numerator? How do you expand (a + b)^2?

 

[Saladsamurai]

um the course I am taking told me first multiply the numerator and denominator by
sqrt(x^2+5) - 3

i might have done it wrong but then i got x^2+5-9/x-2(sqrt(x^2+5) - 3)
i factored that to x^2-4/x-2(sqrt(x^2+5) - 3)
and then eventually got (x-2)(x+2)/x-2(sqrt(x^2+5) - 3)
canceled out x-2
x+2/sqrt(x^2 + 5) - 3
then subtituted the x for 2
thats how i got that answer...i think that's how the teacher told me to do it...probably made mistakes along the way though..im not sure

Your on the right track by using the conjugate; however, you need to watch your signs
the conjugate of \sqrt{x^2+5}-3 is \sqrt{x^2+5}+3

Casey

PS~Do you understand why the sign needs to be a plus (+) sign?
Hint: (a+b)^2 does not = a^2+b^2
Casey