Question

Evaluate the limit
lim (25-b)/(5-√b)
b-->25

Answer 1

factor the numerator; something will cancel

Answer 2

remember the difference of squares formula\[a^2-b^2=(a-b)(a+b)\]

Answer 3

i tried to factor but it didn't work?

Answer 4

what did you factor the numerator into?

Answer 5

5.5-b?

Answer 6

not sure where you got 5.5 from
use the formula for difference of squares I worte above\[a^2-b^2=(a-b)(a+b)\]what is \(a\) in your case?
what is \(b\) ?

Answer 7

wrote

Answer 8

a=5
b=b?

Answer 9

a=5 yes
but in your formula b^2=b (bad notation choice on my part, sorry, different b's)
so when you factor it a=5 and b=√b

Answer 10

(5-b)(5+b)

Answer 11

let me rephrase the difference of squares formula to avoid confusion...

Answer 12

in the form \[p^2-q^2\]we can factor this into\[(p-q)(p+q)\]you have, in the numerator\[25-b\]so what is p^2 ?
what is q^2 ?


based on that, what is p and what is q ?
then write your expression

Answer 13

is it (5-b)(5+b)?

Answer 14

not quite
what is q^2 in your expression?

Answer 15

5?

Answer 16

no, that is p
let's compare your equation with the form for difference of squares\[p^2-q^2=(p-q)(p+q)\]\[25-b=?????\]so we can see that \(25=p^2\), which means that \(p=\pm25\)
now what about \(q^2\) what does that correspond to in your formula?

Answer 17

typo above
*which means that \(p=\pm5\)

Answer 18

ok how about q^2?

Answer 19

b^2

Answer 20

let us make a comparison