Question

Evaluate the limit
\lim_{ x \rightarrow 3 } \frac { x - 3 } {x^2 + 4 x - 21 }

Answer 1

well, what is the 'value' at x=3?

Answer 2

if its 0/0 then we know that the linear is a factor of the quadratic, and can be removed

Answer 3

its evaluate the limit..... x -> 3
x-3/x squared + 4x -21

Answer 4

yeah .... the question is readable. evaluate it at x=3, if you get 0/0, then factor out the linear and youll have an equivalent function to play with

Answer 5

i dont understand example if possible???

Answer 6

let x=3, what are the values for top and bottom?

Answer 7

\[\lim_{ x \rightarrow 3 } \frac { x - 3 } {x^2 + 4 x - 21 }\]
What is the outcome when you use x=3?

Answer 8

0/0

Answer 9

good, then the bottom has a factor of (x-3) in it ... factor it out and cancel it

Answer 10

????

Answer 11

you cover polynomials before you cover rational expressions

you should have already covered how to factor a quadratic

Answer 12

derivative?

Answer 13

no, factors

(x+a)(x+b) = x^2 +(a+b)x + ab

Answer 14

i know what you mean now

Answer 15

:) i knew you had to have known at least at some point

Answer 16

so what we have is:

(x-3)
--------------
(x-3)(something)

which is why when x=3, the top and bottom go to zero, if we factor the bottom and cancel

1
--------------
(something)


we have something that will tell us the limit since we were able to remove the offending zero

Answer 17

after factoring i got 3 and -7

Answer 18

those are roots, but the factored form is one step less than finding roots but fair enough

x^2 + 4 x - 21

(x-3) (x+7)

therefore: 1/(x+7) is our equivanelt function that we can assess the limit with

when x=3, what do we get :)

Answer 19

1/10

Answer 20

thanks lad

Answer 21

youre welcome ;)