Thread: limit does not exist

skectch the graph y=cos(pie/x) over the interval (-.1,0.01)
the calculator comes up with an inaccurate graph. We have been studying sequences and I'm sure using them is the key to solving this problem.

THis is for my calc. 2 class.

Originally Posted by horsejumper

skectch the graph y=cos(pie/x) over the interval (-.1,0.01)
the calculator comes up with an inaccurate graph. We have been studying sequences and I'm sure using them is the key to solving this problem.

THis is for my calc. 2 class.

Hello,

the function is not defined for x = 0. you'll find all further considerations in the attached image:

ok i can do that but the next question asks, how many times does the function osxillate between -1 and 1.
How do i figure that out?

Originally Posted by horsejumper

ok i can do that but the next question asks, how many times does the function osxillate between -1 and 1.
How do i figure that out?

Hello,

take the limit with z → ∞. If z is an integer cos(π*z) is either 1 or -1. If z → ∞ there are unlimited many times of oscillation