Question

find the limit x->infinity of arctan(x-x^4)

Answer 1

this is indeterminate, right?

Answer 2

let y = lim arctan ( x-x^4) , so take tan of y
tan (y) = tan ( lim arctan (x-x^4)) = lim (tan (arctan ( x-x^4)) = lim x-x^4

Answer 3

i would go like this:
lim arctan(x( 1- x^3))

Answer 4

im from waterloo too

Answer 5

then we have arctan(-infinity)=-pi/2

Answer 6

this make sense?

Answer 7

hmmmm i see got it thx,

Answer 8

k np

Answer 9

what about b, im having trouble eliminating the sart sign

Answer 10

this is a great site- i find the smartest ppl are on between 10pm and midnight, and prob like 9am-noon

Answer 11

mwgc, isnt that indeterminate though?

Answer 12

i went and took 9x^6 out of the sqrt so then we have

3x^3(sqrt(1-x/9x^6))

Answer 13

mg, no this problem
l
imit x->infinity of arctan(x-x^4)

Answer 14

then factor out x^3 outta the bottom

Answer 15

what?

Answer 16

he/she is talkin now about part b of this question which is on our assignment

Answer 17

i dont see part b)
can we talk about part a) please

Answer 18

i dont really see how you got 3x^3(sqrt(1-x/9x^6))

Answer 19

arctan ( x - x^4) is indeterminate , arctan (-oo - oo ). oh wait

Answer 20

sqrt(9x^6) is 3x^3

Answer 21

, it isnt indeterminate, it is arctan -oo

Answer 22

OMG LMAO OMFG

Answer 23

then when we multiply it, its multiplied by sqrt(1- x/9x^6)

Answer 24

we divide the second term to cancel out that multiplication

Answer 25

ya @barry so -pi/2

Answer 26

oo - oo is indeterminate, but
-oo - oo is NOT indeterminate

Answer 27

yo @mwgc, what is part b), i dont see it bro

Answer 28

ill post it

Answer 29

lim x->infinity
(sqrt(9x^6-x))/(x^3+1)

Answer 30

its negative infinity

Answer 31

how did u get that i got 3

Answer 32

lim sqrt ( 9x^6 -x ) / ( x^3 + 1) = sqrt ([9x^6] ( 1 - 1/(9x^5) ) / ( x^3+1) = 3 |x^3| sqrt ( 1 - 1/(9x^5))/(x^3 + 1)

Answer 33

3x^3sqrt(1- x/9x^6)/x^3(1-1/x^3)

3(sqrt(1-1/9x^5)/1-1/x^3

plug in infinity for x

Answer 34

right barry is right, use absolute values for takin outta sqrt

Answer 35

in this case tho doesnt matter

Answer 36

. well... it kinda does, but it doesnt effect the solution no

Answer 37

cuz |positive infinity| is positive infinity

Answer 38

i thought he wanted negative infinity. sorry

Answer 39

o crap! sry veryconfused i thot you were saying the answer was -infinity, youre right we are lookin at x->-infinity

Answer 40

doesnt the answer become -3 then

Answer 41

veryconfused u there?

Answer 42

ya im workin out the question right now and i did get -3

Answer 43

k good i already handed mine in so i said positive 3 o well

Answer 44

lol

Answer 45

k man gnite

Answer 46

night