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yeah..i'm pretty sure we learned this in calc.
you cant include the end points,
in order to be continuous the function has to be defined at the point and have a limit at the point, and the two must equal each other.
x=-4, has not limit from the LHS, it cant be continuous, should be an open bracket
there is no open circle on 4
(-4,-2) , but they dont give that as an option
wat does it mean if there is no corcle at the end of something?
it means it includes that point
so wud that be open or closed?
but there is nothing to the left of it , there is no LHS limit
there is no way to approach x=-4 from the negative x axis , because its not defined , so strictly speaking it shouldnt be continuous there ( even though the answer doesnt give (-4,-2) as an interval that you can choose
sadas answrs were correct tho
yeh, but what was this ?, a online assignment site? , I am smarter than those computers
hahaha yeah it is
i just dont get waht it means when ther is no circle at the end of a line
eg when x=4
lol wud u know dumbcow?
when x=4, the function tends to infinity, therefore, there is no limit there, and if there is no limit, it cannot be continuous at that point.
but the answer was (4,6).....this implies that at 4 its open?
yes. it is open because it is not strictly defined at that point.
okay so it continues at that point right?
it is only continuous if it has a limit everywhere and if it is defined everywhere.. in the case of x=4, the limit tends to infinity (which means there is no real limit) so therefore, it cannot be continuous.
oh but the q asked for which interval is it continous?
yes, and that was elec's point.
lol im confused
The definition of continuity I was taught at uni was , has right hand side and left hand side limits equal and they must equal the function value
which point are you confused about and?
that if at x=4 is not continous how come the interval of (4,6) is continous
because we are using open brackets on both sides..with open brackets, you are not including the x=4 or the x=6 in your answer.
you need to learn your notation correctly
so basically at the end of 4 is an open bracket then
on the intervals [4,6) or (4,6] or [4,6] the function would be discontinuous
you just have to get use to interval notation
and..yes .. basically.
haha lol.ty sadas. which uni u go too elecengineer?
fair enuf. which high school did u go too?
south sydney high school , in maroubra, I live like 10minutes away from the uni
you porbably never heard of the school, its not really famous for anything , just an average school
cool.. i went to hurlstone agricultural high. ever heard of it b4 ?lol