# Thread: Need help with limits

1. ## Need help with limits

Hiya,

how would I calculate lim f(x)/g(x) =12/5 given that g(5)=0
..............................x->5

I tried (x-5) must be a factor of g(x) then made up (5x+1)(x-5) expanded while keeping f(x) at 2x^2+a , then i tried splitting up 2x^2+a into the 5x^2-24x-5 so got (5x^2 -24x-5)-3x^2+24x+5+a but going around in circles...

can someone confirm whether im doing this right please ? any steps ? thank you so muchhh

2. ## Re: Need help with limits

i kinda wanna know cuz im practising as i have exams soon so any advice appreciated ! so please can i have an explanation with methods steps shown so i understand how i can do it in the exam and my mates dont know and its the holidays so i cant ask the teacher and i kinda have a lot to get through

stressful so much i need to study!

hope you understand,
thank you

3. ## Re: Need help with limits

what are $f(x)$ and $g(x)$ ?

4. ## Re: Need help with limits

Originally Posted by romsek
what are $f(x)$ and $g(x)$ ?
Hiya, tysm for the response - I have to find f(x) and g(x), the purpose, sorry if i hadnt made myself clear.

thanks!

5. ## Re: Need help with limits

$\displaystyle \lim_{x \to 5} \dfrac{x^2+2x-35}{x^2-5x} =$ ?

6. ## Re: Need help with limits

Originally Posted by DiscreteMathHelp
Hiya, tysm for the response - I have to find f(x) and g(x), the purpose, sorry if i hadnt made myself clear.

thanks!
well let's see

$\displaystyle \lim_{x\to 5}~\dfrac{f(x)}{g(x)} = \dfrac {12}{5}$

and $g(5)=0$

yes, $g(x)$ must contain a factor of $x-5$

so the slickest thing to do is set

$f(x)=f_1(x)(x-5)$

where $f_1(5) = \dfrac{12}{5}$

$f_1(x) = \dfrac {12}{5} (6-x)$ will do this nicely so we end up with

$f(x) = \dfrac{12}{5}(6-x)(x-5) = \dfrac 1 5 (-12 x^2+132 x-360)$

$g(x) = (x-5)$

or we might as well have

$f(x) = -12 x^2+132 x-360$

$g(x) = 5(x-5)$

7. ## Re: Need help with limits

Notice that romsek chose g(x) to be x- 5 and chose " $f_1(x)$" to be $\frac{12}{5}(6- x)$. There are an infinite number of functions f(x) and g(x) that would work.

8. ## Re: Need help with limits

Originally Posted by HallsofIvy
Notice that romsek chose g(x) to be x- 5 and chose " $f_1(x)$" to be $\frac{12}{5}(6- x)$. There are an infinite number of functions f(x) and g(x) that would work.
yeah but I didn't like any of the others, too tinny.

9. ## Re: Need help with limits

Originally Posted by romsek
yeah but I didn't like any of the others, too tinny.
tysm
honestly i really appreciated it, also i needed both that had degree 2 so i just timed both the equations by x, as i suppose as i should do...

this seems like a really great forum, you guys saved me in an exam once before cuz something really similar came up !