lim x → ∞ 3 cos x =?

Question

lim  x → ∞  3 cos x =?

xapproachesinfinity · Answer

what do you know about cosx graph

xapproachesinfinity · Answer

anything?

anonymous · Answer

it goes  to positive and negative ?

xapproachesinfinity · Answer

hmm well... beside that?

xapproachesinfinity · Answer

alot of function do what you said what is special about cosx?

anonymous · Answer

im not that good with trig

xapproachesinfinity · Answer

http://hotmath.com/hotmath_help/topics/graphing-cosine-function/cos-graph.gif

xapproachesinfinity · Answer

that is  cosx graph what do you observe?
anything different from other functions that you are familiar with

anonymous · Answer

the vertical lines

xapproachesinfinity · Answer

not really
don't you see that the graph is oscillating btw -1 and 1

xapproachesinfinity · Answer

so as we proceed to oo does y=cosx get to any specific value?

xapproachesinfinity · Answer

this require a good understanding of limit so i take it that you learned about limits?

anonymous · Answer

yea

xapproachesinfinity · Answer

so can you tell does the graph then to some value or not
that's what we study when talk about limits
think of what is happening as x goes  to oo
what happens to the graph does it tend to some value?

xapproachesinfinity · Answer

if you paid attention i already mention what the graph does

anonymous · Answer

it changes from + to -

xapproachesinfinity · Answer

not just + and -
that is not our concerned
it oscillates between -1 and 1

xapproachesinfinity · Answer

sometimes it goes to 1 sometimes to -1
as we proceed to oo the same thing repeats because cos is a periodic function
this true for other periodic functions as well

xapproachesinfinity · Answer

you need to review the limits again
in this case what is happening is there is not limit
sometimes its -1 sometimes its 1 so the limit does not exist

anonymous · Answer

ah ok i see

xapproachesinfinity · Answer

if you understand the limits then this should be really easy to get
3 that is attached to cosx doen't affect the result
we have the theorem limit of the product is the product of the limit
so we can alwyas think of the limit as 3limit x to oo (cosx)
since limit x to oo (3) is just 3

anonymous · Answer

oh ok thanks, ill review it more, trig always confuses me

xapproachesinfinity · Answer

well there is no helping it you have to review it too
calc involve a lot of trig

anonymous · Answer

yea

xapproachesinfinity · Answer

just practice :)