Question

Use the given graph to determine the limit, if it exists.

A coordinate graph is shown with a downward sloped line crossing the y axis at the origin that ends at the open point 3, negative 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, negative 4.

Find limit as x approaches three from the right of f of x..

Answer 1

do you see on the x-axis the number 3?

Answer 2

your thingy says hey let's look at the right of x=3
and see where are the y's
what are the y's approaching

Answer 3

is the answer -4?

Answer 4

yes! :)

Answer 5

that is exactly right
as we approach x=3 from the right
we approach y=-4

Answer 6

Thank you very much!

Answer 7

np

Answer 8

do you know what the left limit of x=3 would be ?

Answer 9

-1?

Answer 10

yep yep

and you would say the actual limit would not exist
that is:
\[\lim_{x \rightarrow 3^-} f(x)=-1 \\ \lim_{x \rightarrow 3^+}f(x)=-4 \\ \lim_{x \rightarrow 3}f(x) \text{ does not exist }\]

Answer 11

woo yay! Thank you again

Answer 12

np
your welcome
have fun with calculus