Question

Suppose f(x) --> 150 and g(x) -->0 with g(x)<0 as x--> 3. Determine lim as x-->3 f(x)/g(x).

Answer 1

lim (f/g) = 150/(some really small negative number) = -infinity

you can make up a table for y = 150/x for values of x < 0 and you'll see y becoming a larger and larger negative number

Answer 2

@jim_thompson5910 I don't understand why you do 150/x though.How am i supposed to know to ignore g(x)-->0 and put in x, but for f(x) just use 150? Thanks

Answer 3

well since f(x) --> 150 as x--> 3, this means that the limit of f/g will have you replace f with 150

the same will apply to g(x) as well...but you'd get 0 in the denominator, which is undefined

Answer 4

so what you have to do is use a table to see what happens to the y values as x gets closer and closer to 0

you use the equation y = 150/x to make the table

Answer 5

and you'll be looking at x values less than 0

Answer 6

Right that makes sense, so as x gets further and further away from 0 (more negative), y gets closer and closer to 0, but still negative just very small. Is that the right way to think about it?

Answer 7

Since if x=-1, then y=-150. If x=-2, then y=-75, and so on?

Answer 8

but you're getting x closer and closer to 0

Answer 9

if x = -1, then y = -150

if x = -0.1, then y = -1500

if x = -0.01, then y = -15000

if x = -0.001, then y = -150000

etc etc

Answer 10

Oh, why is x getting closer and closer to 0?
Also whats the point of x--3? Seems irrelevant to the problem.

Answer 11

no it's relevant, I'm just referring to g(x) as x

Answer 12

basically it should be

as g(x) ---> 0, f(x)/g(x) ---> -infinity

since g(x) < 0

Answer 13

Nevermind i understand why we do smaller x values getting closer to 0. However i still dont understand x--> 3

Answer 14

I was using y = 150/x because it's easier to write out

Answer 15

I got that part, but whats the 3 have to do with anything.

Answer 16

not much really, all we care about is what f(x) and g(x) are approaching

Answer 17

Thats what confuses me. It makes sense though now, Thanks, i appreciate it.

Answer 18

the only thing the x --> 3 has to do with is the fact that f(x) ---> 150 as x ---> 3 and g(x) ---> 0 as x ---> 3

Answer 19

then they ask

what does f/g approach as x ----> 3

Answer 20

so that's the only real use of the "x ---> 3" part

Answer 21

Oh okay, since g(x) is limited by g(x)<0, the 3 could be replaced by any positive number really, and the problem would be the same.

Answer 22

yeah you could easily replace all the '3' numbers with '10' or something and it wouldn't matter

Answer 23

Gotcha, Thanks again.

Answer 24

same with 150 since that doesn't affect the answer of -infinity either

Answer 25

yw