Question

Find the limit

f(x) = -(x^2)/(x+3)

a) lim f(x)
x-3^-

b) lim f(x)
x-3^+

c) lim f(x)
x-3

I know that a is dne because of the graph and that b is -infinity. And that c is dne because they are not the same. But I do not know how to do this algebraically. Thank you

Answer 1

It helps to look at the graph of
y = - x^2/(x+3)

http://www.wolframalpha.com/input/?i=plot+y+%3D+-(x%5E2)%2F(x%2B3)

look at the second graph, the first one is a close-up of the second.

The "forbidden" value is x = -3

now look at just a bit to the right of x = -3
What does the graph do ?
What does the graph do just a bit to the left of -3 ?

you might also want to use your calculator and evaluate -x^2/(x+3) when x = -3.01 and -2.99 as an example

for x = -3.01,
y = + 906.01

now try x = -2.999
y = -8994.001

use you calculator to get even closer to -3 from both sides

Answer 2

AB ☍ CD

Answer 3

AB ▒ CD

Answer 4

AB ∥ CD