Question

Evaluate the limit using l'Hopital's Rule
(I tried this, but I can't figure out where I went wrong :/)
lim(y->pi/2)((pi/2)-y)

Answer 1

lim(y−>π/2)(π2−y)\[\lim(y−>π/2)(\frac{ \pi }{ 2 }−y)tany\]

Answer 2

ignore the first part

Answer 3

@jim_thompson5910 if you can help, it would be greatly appreciated :)

Answer 4

@dan815

Answer 5

@tkhunny

Answer 6

In what state is in an Indeterminate Form?

Answer 7

what

Answer 8

Not a good response.

In order to utilize l'Hospital's Rule, you must have an Indeterminate Form. Do you?

Answer 9

Well I would've said California, but I figured that that was the wrong answer :3
Yes we do have an indeterminate form

Answer 10

Prove it. It's not obvious.

Answer 11

0 times infinity

Answer 12

That doesn't contain a Numerator and Denominator, which is where the rule is useful. Is there a firm like that?

Answer 13

* form

Answer 14

Yes there is. You have to rewrite with an LCD

Answer 15

Then you get a fraction

Answer 16

Show me.

Answer 17

Its what my teacher told me to do

Answer 18

Okay. Show me.

Answer 19

Oh wait, thats infinity-infinity

Answer 20

For this one, its with natural logs

Answer 21

so you take the natural log of the inside part

Answer 22

Then the exponent can be rewritten as a multiplier

Answer 23

Then you rewrite as a fraction

Answer 24

Are we talking about the same problem?

\(\lim_{x\rightarrow \pi/2}\left(\pi/2 - y\right)\cdot \tan{y}\)

Answer 25

Yes

Answer 26

Sorry, 'y', not 'x'.

Answer 27

Wait i was wrong again

Answer 28

Sorry

Answer 29

Then why not just \(\dfrac{\pi/2 - y}{\cot(y)}\)? This gives the form 0/0.

Answer 30

This is the one where you rewrite as division

Answer 31

Don't get hung up on techniques. Get hung up on when the rule is applicable and then just get it where it is useful.

Answer 32

I did\[tany/(1/((\pi/2)-y)))\]

Answer 33

Which is infinity over infinity

Answer 34

Then I l'hopitaled

Answer 35

And got sec^2x/(-1/((pi/2)-y))^2)

Answer 36

And I got hung up because thats infinity over infinity as well, and l'hopitaling again wouldn't help me in any way

Answer 37

Well, that's ONLY because you chose poorly when you moved something to the denominator. You already have a linear factor in the numerator. That will vanish with the first derivative. Don't move it. Move the tangent to the denominator.

Answer 38

I didn't realize that there were rules for choosing

Answer 39

The sign was wrong, too. But you can worry about that, later.

Answer 40

We only worked with x's as the multiplier. Then you could just rewrite those as 1/x

Answer 41

There are not rules for choosing. Don't get hung up on such things. You can, however, choose wisely in many circumstances.

Answer 42

I just assumed to do the term with the x in it

Answer 43

Yup. It got you nowhere. Move the tangent and give it a go.

Answer 44

k

Answer 45

I got -y/-csc^2y

Answer 46

So thats

Answer 47

pi/2/0

Answer 48

so infinity

Answer 49

-y? Try that numerator, again.

Answer 50

oh snap

Answer 51

-1. sorry bout that

Answer 52

And of course I messed up the unit circle. Its 1

Answer 53

Thank you so much for your help. How do you decide which part to pick to rewrite as division?

Answer 54

It's not always obvious. With a little smirk on my face, you pick a way that is useful. :-) If you find that one way is not useful, try something else.

Answer 55

What did you get for the final answer?

Answer 56

So basically the same thing as integration by parts XD

Answer 57

1

Answer 58

Perfect. Good work.

Answer 59

Fair enough. Keep in mind what you will be differentiating. If you only make things more difficult, that's not likely to be helpful. Keep up the good work.

Answer 60

Thank you very much!