Question

Lim √(x)/(x-9)^4 when x goes to 9. Someone know how to do this without L'Hôspital ?

Answer 1

\[\sqrt{x}/ (x - 9)^4\]

Answer 2

??

Answer 3

Yes

Answer 4

it's just going to be infinity

Answer 5

Yeah. Sonofa_nh is right.

Answer 6

When I could stop trying simplify the limit, and conclude that it is gong to infinity?

Answer 7

You can't use L'hopital on this since \[\lim_{x\rightarrow9}\sqrt{x}=9\neq0 \quad \text{ or }\quad \pm\infty\]

Answer 8

\[\lim_{x\rightarrow9}\sqrt{x}=3\neq0 \quad \text{ or }\quad \pm\infty\]

Answer 9

in order to use l'hospitals rules both numerator and denominator have to be 0 or infinity

Answer 10

in this question the numerator does not work so u can't use it

Answer 11

However, when you take the limit, you'll get \[3/\left(\lim_{n\rightarrow9} (x-9)^4\right)\]Note that the bottom rapidly approaches 0 from both sides, so you end up with\[\frac{3}{\text{Very small positive number}}\]This will go off to infinity.

Answer 12

if \[x \rightarrow9\] then \[x-9\rightarrow0\]
hence the expression tends
\[F(x)\rightarrow \infty\]