Question

determine the limit as x->0 [(sinx)/((x^2) -x)]

Answer 1

\[\lim_{x \rightarrow 0} \frac{ sinx }{ x ^{2}-x}\]

Answer 2

differentiate top/bottom then re-evaluate limit

Answer 3

can you answer my question that i posted 22 hours ago dumbcow?

Answer 4

@dumbcow what does that mean?

Answer 5

i can look at it...send me the link

Answer 6

umm im kinda new to open study so i will just type it

Answer 7

Benjamin's personal trainer recommended that he record his calories during the day. The bar graph shows the number of calories contained in each meal. Which of the following is true? Breakfast- 350 lunch- 400 dinner- 250 snacks- 200 Snacks made up fifty percent of his calorie intake. or Breakfast and snacks made up less than half of his calorie intake. or He ate food containing two thousand calories during the day shown. or During two of his meals, he ate food containing the same number of calories.

Answer 8

sorry i didnt space anything

Answer 9

@ses11 , its called L'hopitals rule
any limit that goes to 0/0 can be reevaluated if derivative is taken of both top/bottom seperately

Answer 10

@mathgenius14 , please delete question, i will find your post and discuss it there
this is @ses11 post

Answer 11

@dumbcow ok this is my math summer packet for going into calc and i havent learned most of this stuff yet, so how do i do a derivative of the fraction?

Answer 12

oh well if you dont know derivatives yet...you have a problem :)

Answer 13

there are other ways but L'hopitals way is usually easiest

Answer 14

haha yeah it has been a struggle so far

Answer 15

how does l'hopitals rule work?

Answer 16

hmm lets do the old fashion approach...plug in really small values for "x" that get closer to 0 and see where it converges
-make a table

x f(x)
0.1
0.01
0.001
...

Answer 17

if you are not in calculus yet, there is no point in going over l'hopitals yet :)

Answer 18

ok so as x gets smaller the numerator keeps getting bigger and the denominator keeps getting smaller and negative?

Answer 19

numerator should get smaller ? sin(0) = 0 , sin(.1) > sin(.001)

Answer 20

anyway don't worry about what each num/denom is doing, what is f(x) doing

Answer 21

gotta go .... you should see f(x) get closer to -1

limit = -1

Answer 22

were you taught lhopitals rule

Answer 23

0/0 interminant form so you can use l hospitals rule

Answer 24

@dan815 no i don't know what that is

Answer 25

ok

Answer 26

well dont worry l hospitals rule isnt so scary

Answer 27

you can derive it from first principles

Answer 28

have you learnt about derivative yet

Answer 29

@dan815 no i havent really learned derivatives either

Answer 30

oh i see

Answer 31

well in that case no calculus

Answer 32

plug and chug my friend

Answer 33

you can try think this way

Answer 34

what is the rate sin x is going toward 0 and
what is the rate x^2-x going towards 0

Answer 35

if sin x goes towards 0 must faster than x^2-x then it will be zero since
sinx/x^2-x is your function
but if x^2-x is going towards 0 must faster than sin x then it will be infinity
or if they seem to have some proportional rate, it will equal a constant

Answer 36

ok so plugging in numbers will tell me this?