Question

need help

Answer 1

is it:
f(x)=cos(x) , -pi<=x<=pi
?

Answer 2

yes

Answer 3

this is the graph:

http://www.wolframalpha.com/input/?i=graph%28f%28x%29%3Dcos%28x%29+%2C+-pi%3C%3Dx%3C%3Dpi%29

Answer 4

lim(x->0) f(x) = 1

lim(x->pi/2-) = 0

lim(x->pi/2+) = 0

Answer 5

note that questions #2 and #3 are identical

Answer 6

That's why there are only 3 answers above instead of 4.

Answer 7

so does question 2 and 3 exists?

Answer 8

Your questions were:
1) lim(x->0) f(x) and the answer is limit exists and = 1
2) lim(x->pi/2-) f(x) and the answer is limit exists and = 0
3) lim(x->pi/2-) f(x) and the answer is limit exists and = 0
4) lim(x->pi/2 ) f(x) and the answer is limit exists and = 0

Answer 9

as you can see question #2 and #3 are the same.

Answer 10

actually on question three there was suppose to be a plus sign after pi/2

Answer 11

ok - so here it is with the + sign:

3) lim(x->pi/2+) f(x) and the answer is limit exists and = 0

Answer 12

why is the first answer number 1

Answer 13

The + sign means we are checking the limit as we are approaching from the right side
The - sign means we are checking the limit as we are approaching from the left side

Answer 14

oh, I get you plug 0 into cos which give you 1

Answer 15

As to why the answer to #1 is 1, look at the graph.
Which value does f(x)=cos(x) approach as you get very close to x=0 ?

Answer 16

Did you click the link I posted above, which shows the graph ?

Answer 17

so is this problem wanting us to find the value f(x) or want us to see if its approaching negative infinite or positive infinite

Answer 18

note that pi/2 is roughly 1.57 . you can see that intersting things happen to the graph at the points where x=-pi/2 , x=0 and x=pi/2 .

As to your question - there was no mention at all of anything approaching infinity.
The questions asked what happens to f(x) when x approaches 0,
and when x approaches pi/2 (from the left and from the right).

Answer 19

oh ok, so the limit x approaches pi/2 from the left is zero? Same can be said for the right side to, correct?