Question

LIMIT SIN^2(X)/X(1+COS(X) AS X GOES TO 0

Answer 1

\[\lim_{x\rightarrow 0}\frac{\sin^2x}{x(1+\cos x)}\] is it correct?

Answer 2

YES

Answer 3

zero

Answer 4

is the answer

fairly sure

Answer 5

its not a indeterminate form , we can just sub in x=0

Answer 6

Ok, answer is 0, but this is indeterminate form 0/0

Answer 7

ahh yeh , im an idiot , didnt see the x factor on the bottom

differnetiate top and bottom and try again

Answer 8

YES I GOT 0/0 BUT MY TEACHER MARK MY PAPER STILL WRONG WITH MY STEPS I JUST SUBSTITUTE X FOR 0

Answer 9

\[=\lim_{x \rightarrow 0}\frac{\sin x ^{2}}{x} * \lim_{x \rightarrow 0}\frac{1}{1+\cos x} = \lim_{x \rightarrow 0}2\sin x \cos x * \frac{1}{2} = 0\]

Answer 10

so [ 2sinxcosx ] / [ x(-sin(x) ) + (1+cos(x)) ]

2sin(x)cos(x) / [ 1 +cos(x) -xsin(x) ]

Answer 11

now when you sub x=0 , it isnt indeterminate , and we do get 0 as the final answer

Answer 12

dumbcow,
\[\lim_{x\rightarrow a}f(x)g(x)\neq\lim_{x\rightarrow a}f(x)\cdot\lim_{x\rightarrow a}g(x)\]

Answer 13

^doesnt it?

I thought I remember reading somewhere that it does

Answer 14

really? are you sure
lim x^2 as x->2 is 4
limx * limx as x->2 is 2*2=4

Answer 15

no they can be separated, see below
http://tutorial.math.lamar.edu/Classes/CalcI/LimitsProperties.aspx

Answer 16

YES GUYS YOU CAN SEPARATE IM SURE OF THAT

Answer 17

before you answer, shut the caps button off LOL!

Answer 18

oh well ~