# Thread: find the functions f and g such that

1. ## find the functions f and g such that

find the functions $\displaystyle f$ and $\displaystyle g$
$\displaystyle \lim_{x \to c}{f(x)} = \infty$ and $\displaystyle \lim_{x \to c}{g(x)} = \infty$

but

$\displaystyle \lim_{x \to c}{[f(x) - g(x)]} \ne 0$

2. Originally Posted by bigwave
find the functions $\displaystyle f$ and $\displaystyle g$
$\displaystyle \lim_{x \to c}{f(x)} = \infty$ and $\displaystyle \lim_{x \to c}{g(x)} = \infty$

but

$\displaystyle \lim_{x \to c}{[f(x) - g(x)]} \ne 0$
$\displaystyle f(x)=\frac{2}{x-1},g(x)=\frac{1}{x-1},c=1$

EDIT: Actually, to be one-hundred percent accurate you should actually consider $\displaystyle |f(x)|,|g(x)|$

3. If you want a finite limit for the difference you could consider $\displaystyle f(x)=\frac{ax^2}{x^2-1}$ and $\displaystyle g(x)=\frac{a}{x^2-1}$ then $\displaystyle f(x)-g(x)=a\frac{x^2-1}{x^2-1} \rightarrow a$

4. looks like there are multiple answers to this

what would be the simplest version of $\displaystyle \frac{1}{x}$ that could be used with this. in that it looks like we must have an x in the denominator.