Question

Use graphs and tables to find the limit and identify any vertical asymptotes the function.
LAST QUESTION @ganeshie8

Answer 1

Use graphs and tables to find the limit and identify any vertical asymptotes the function.

Answer 2

please show how to do it because this is a practice problem thats gonna be on future tests

Answer 3

the way I would start by expanding the denominator \((x-10)^2\)

Answer 4

(x-5)(x+5)

Answer 5

expanding it you should find \[(x-10)^2=x^2-20x+100\]

Answer 6

ohh

Answer 7

so, we have \[\frac1{x^2-20x+100}\]
we can separate this to
\[\frac1{x^2}-\frac1{20x}+\frac1{100}\]
if we consider the limit, we should get (1/0) (1/0) and 1/100 so the limit at 0 would be \(\frac1{100}\)

Answer 8

i got it, thanks

Answer 9

going back to the original:
\[\frac1{(x-10)^2}\] we know that it will never be able to be y=0 because that would be an undefined value of x, so there is a horizontal asymptote at y=0.
we can also see that for x=10 the bottom is again impossible so there is a asymptote there.
Namely, asymptotes are:
\[\frac1{(x-10)^2} \rightarrow 0 ~~~~\text{as}~~~~x\rightarrow\pm\infty\\ \frac1{(x-10)^2} \rightarrow \infty ~~~~\text{as}~~~x\rightarrow10\]