Question

The question is attached.

Answer 1

does the top factor into (x^2+25)(x^2-25)

Answer 2

\[\lim_{x \rightarrow -5}\frac{ x^4-625 }{ x+5 }=\lim_{x \rightarrow -5}\frac{(x^2-25)(x^2+25)}{ x+5 }=\lim_{x \rightarrow -5}\frac{ (x+5)(x-5)(x^2+25)}{ x+5 }=\]\[=\lim_{x \rightarrow -5}(x-5)(x^2+25)=-10 \times 50 =-500\]

Answer 3

the question is: which low explain the first action?

Answer 4

and the next one and so on.

Answer 5

can you rephrase the question. I don't understand the "low"

Answer 6

law
sorry.

Answer 7

Factorization of polynomials

Answer 8

this option is not in the image .

Answer 9

Now I know. The option is this one: functions agree near the limit point.

Answer 10

I do not know other name for this but I woud choose product law

Answer 11

Steps 1 and 2: Product Law
Step 3 Quotient Law
Step 4 Limit Law
Step 5 Arithmetic

Answer 12

looks good to me!

Answer 13

However, in limits theory, quotient law states:\[\lim_{x->a}\frac{ f(x) }{ g(x) }=\frac{ \lim_{x->a} f(x) }{ \lim_{x->a} g(x)}\] and this is nothing we gone through here

Answer 14

https://mooculus.osu.edu/exercises/limitsSymbolic

first and second: functions agree near the limit point.
third: sum law.

Answer 15

Or product law, because in the end we have said:\[\lim_{x->-5}(x-5)(x^2+25)=\lim_{x->-5}(x-5)·\lim_{x->-5}(x^2+5)=-10 \times 50=-500\]

Answer 16

yes there are more steps, in the end the answer could be that one.