Question

limit

Answer 1

\[\LARGE \lim_{x \to 0^{+} }\frac{1-cosx-xsinx}{\sin^{2}x+2cosx-2}\]

Answer 2

I though it was in the form (0/0) so, applied L'hospital...

Answer 3

just put 0 where x is

Answer 4

on calculator

Answer 5

sorry I don't get calculators on exams

Answer 6

it is 0/0
what u get after L'H rule?

Answer 7

D:

Answer 8

getting same

Answer 9

denominator still =0
what about numerator ?after applying LH rule?

Answer 10

\[f(x) = -sinx-(x-cosx+sinx)\]\[g(x) = (2)(sinx)(cosx) + 2(sinx)\]

Answer 11

what have you done to numerator :O
derivative of cos x is - sin x
and
for x sin x, you'll need product rule

Answer 12

same for denominator
derivative of cos x is - sin x

Answer 13

how did u get x-cosx+sinx ?

Answer 14

o wait let me fix that\[\frac{(sinx+xcosx-sinx)}{\sin(2x)-2sinx}\]

Answer 15

oh that's -(x*-cosx +sinx)

Answer 16

(x sin x)' = x cos x + sin x

Answer 17

so numerator is just
sin x - x cos x - sin x
which is just
-xcos x
got this ?

Answer 18

\[\frac{cosx+(xsinx +(cosx))-cosx)}{2\cos(2x)-2cosx}\]

Answer 19

yea I used L'hospital again because it was in indeterminate form

Answer 20

you didn't need to apply L'Hopital's again :P
you can but not required

Answer 21

lets try to solve this
\(\large \dfrac{-x\cos x}{\sin 2x - 2\sin x}\)
you got till here ?

Answer 22

= 1+0+1-1/2-2.... what that's not right....

what you have is
-(0+)(1)/(0-0)

Answer 23

yea I got that

If I simplify\[\frac{xsinx+cosx}{2(2\cos^{2}x-1)-2cosx}\]

Answer 24

so just plug in x =0 now

Answer 25

because you don't get 0/0 form now

Answer 26

1/(2(1)-(2))

Answer 27

I got something worse ahhhhh.

Answer 28

you got 1/0 = +infinity

Answer 29

how is that worse ? :P

Answer 30

o well I guess that is my answer..

Answer 31

yup.

Answer 32

another one coming up ;)

Answer 33

the bottom is going to 0 but you would still need to determine if it was from the left or right

Answer 34

Its from the right because the limit is x--->0+

Answer 35

x is coming from the right...what about the expression in the denominator

Answer 36

Well I am sure that the fourth quadrant x is positive. if we approach zero from QI or QIV

Answer 37

is this \[2(2\cos^{2}x-1)-2cosx\] going to zero from the left or right

you need to show that is is coming from the right

Answer 38

so is cosx than

Answer 39

if you give that as an answer...it will be marked wrong.

Answer 40

Oh thanks for worring Zarkon...but its multiple choice so the markers are not picky.