Question

Find the following limits analytically if they exist.

Enter INF for positive infinity and -INF for negative infinity.
If a limit does not exist, enter DNE.

f(x)=x^2+4x−5/x^2+7x−8
(a)lim f(x)=
x→1−
(b)lim f(x)=
x→1+
(c)lim f(x)=
x→1


thanks

Answer 1

f(x)= (x^2+4x−5)/(x^2+7x−8) , I am certain you need brackets in this case
= (x+5)(x-1) / ((x+8)(x-1))
= (x+5)/(x+8) , x ≠ 1

lim (x+5) / (x+8) , as x ---> 1-
= 6/9 = 2/3

lim (x+5)/(x+8) , as x ----> 1+
= 4/7

lim (x+5)/(x+8) , as x ----> 1+

when x = -8, you have a vertical asymptote , when x = -5, you have a zero

I graphed the original and the reduced function, they are the same graph,
except there would be a hole at (1, 2/3)

www.wolframalpha.com/input/?i=f%28x%29+%3D+%28x%2B5%29%2F%28x%2B8%29%2Cf%28x%29%3D+%28x%5E2%2B4x%E2%88%925%29%2F%28x%5E2%2B7x%E2%88%928%29+from++-11+to+4

(open a new window , cut and paste this URL)