Question

Find the horizontal asymptote: (x^2+x-56)/(x+5)

Answer 1

I meant oblique asymptote **

Answer 2

You need to be a sneaky person if you want to do it without a calculator. RIG the expression.
\[\large \lim_{x \rightarrow \infty} \frac{x^2+x-56}{x+5}\]
\[\large =\lim_{x \rightarrow \infty} \frac{x+5}{x+5}+\frac{x^2}{x+5}-\frac{61}{x+5}\]
\[\large =\lim_{x \rightarrow \infty} 1-\frac{61}{x+5}+\frac{x(x+5)}{x+5}-\frac{5x}{x+5}\]
\[\large ==\lim_{x \rightarrow \infty} 1+x-\frac{61}{x+5}-\frac{5(x+5)}{x+5}+\frac{25}{x+5}\]
Now the easy part is here.
The fractions disappear because if you put infinity in the denominator you will basically end up with zero.
\[\huge [=x+1-5\]
\[\huge =x-4\]

Answer 3

Therefore the oblique asymptote is y=x-4.

Answer 4

TO rig the expression, you should just reqrite the denominator on the numerator and then basically add another term to counteract that change. Basically rigging just changes the expression but it does not change the value of the expression.

Answer 5

rewrite*

Answer 6

I know it looks weird if this is your first time seeing this method done, but it works every time. If you have seen this method before, then you should be using this if you cannot simplify the expression any further.