Question

Evaluate the limits

Answer 1

so you know that |x|=x if x>0 and |x|=-x if x<0 correct?

Answer 2

except the highest degree inside the square root is 4
and the highest degree on bottom is 2
so we are dividing both top by sqrt(x^4)

Answer 3

\[\sqrt{x^4}=x^2 \text{ for all x so we don't have to worry about the }\\ \text{ splitting of cases like with } \sqrt{x^2}=|x|\]

Answer 4

you got it from here?

Answer 5

wait so we have to divide both the numerator and the denominator by x^4?

Answer 6

Dividing it by \(\sqrt{x^4} = x^2\)

Answer 7

Follow @freckles explanation.

Answer 8

so how would i rewrite if after i divide by that?

Answer 9

\[\frac{\frac{\sqrt{x^4-8x^3+9}}{\sqrt{x^4}}}{\frac{5x^2-9}{\sqrt{x^4}}}\]

Answer 10

we divided both top and bottom by x^2 because we had the deg of the bottom was 2

Answer 11

we rewrote x^2 as sqrt(x^4) mainly because of the top

Answer 12

sqrt(x^4) though is equal to x^2 for all x

Answer 13

\[\frac{\sqrt{\frac{x^4-8x^3+9}{x^4}}}{\frac{5x^2-9}{x^2}}\]

Answer 14

can you play with this?

Answer 15

and then we can cancel the x^2 next to the 5 right? so the bottom would be?