Hey everybody,
I learned a while back how to do slant asymptotes with polynomials, but I'm having trouble with finding the slant asymptote for:
y = (e^x) - x
ahh I feel so silly. Please help!
Determine the limits of y if x is approaching $\displaystyle \infty$ or $\displaystyle -\infty$:
$\displaystyle \lim_{x \to \infty}(e^x - x) = \infty$ that means there isn't any calculable limit.
Since $\displaystyle \lim_{x \to -\infty}(e^x)=0$
$\displaystyle \lim_{x \to -\infty}(e^x - x) = -x$ That means the graph of the function approaches the line y = -x if x approaches $\displaystyle -\infty$
and that is your slanted asymptote.