In this video, I was explaining how to answer this in terms of rational function end behavior. Most of students in my calc class had me for precalculus as well - we spend a lot of time discussion polynomial and rational function behaviors. Since this function BEHAVES like a rational function whose degree in the numerator is greater than the degree in the denominator, it will not have a horizontal asymptote. Moreover, the right side branch will increase towards infinity as x approaches infinity, and we can say this function will behave the same way.
Agreed. A more appropriate technique here would be to use the Squeeze Theorem since the function cos(x) oscillates between -1 and 1. Generally speaking though, the limit of 1/sqrt(x) is enough to force the overall limit to 0.
But x*cos(x) is unbounded so this example doesn't follow my justification in the video. The squeeze probably explains the behavior of this limit a little better.
These are helpin me mann, final is in 12 hrs
5:03
In example b, infinity over infinity is still infinity?
But then in example c, infinity divides?
Remember; oo/oo=undefined
In this video, I was explaining how to answer this in terms of rational function end behavior. Most of students in my calc class had me for precalculus as well - we spend a lot of time discussion polynomial and rational function behaviors. Since this function BEHAVES like a rational function whose degree in the numerator is greater than the degree in the denominator, it will not have a horizontal asymptote. Moreover, the right side branch will increase towards infinity as x approaches infinity, and we can say this function will behave the same way.
For Q9 d, It is better to use chain rule
he knows he said he just wanted to show how you would do it before learning chain rule
@8:38 the product of infinity times zero is an indeterminate form? Question 9d
Question 9 d
Agreed. A more appropriate technique here would be to use the Squeeze Theorem since the function cos(x) oscillates between -1 and 1. Generally speaking though, the limit of 1/sqrt(x) is enough to force the overall limit to 0.
For d wouldn't a better method be
0
But x*cos(x) is unbounded so this example doesn't follow my justification in the video. The squeeze probably explains the behavior of this limit a little better.
@@mitchehrman just rewatched and you did say bounded my mistake!