Question

Can't solve this on my TI 89 Titanium. The correct answer is -1

Question:
lim as x approaches 90 from the right:
cos(x)/x-90

How can I solve this on my TI 89? It gives me undefined, it just plugs the values in I guess..?

Answer 1

is that
\[\lim_{x \rightarrow 90^+} \frac{\cos(x)}{x-90} ?\]
is this in degrees?

Answer 2

Yes, we've always been using degrees.

Answer 3

does your calculator know you are working in degrees?

Answer 4

Yes, I even tried out all the other modes out of frustration lol

Answer 5

this question is weird
if the answer really is suppose to be -1, there looks like there is a mixture of units going on
.... Like if the question was
\[\lim_{x \rightarrow \frac{\pi}{2}^+} \frac{\cos(x)}{x-\frac{\pi}{2}}\]
this would make more sense

Answer 6

Um, yes it's like that, but since we've always used it as 180/2 then I always assumed it's no difference if I assume it's 90

Answer 7

do you mean the problem was like this and then you change the pi/2 to 90 degrees?

Answer 8

yes

Answer 9

that is probably why your calculator is spitting out undefined then

Answer 10

hm, so how can I make it spit out the right answer?

Answer 11

don't change pi/2 to 90

Answer 12

and stay in the same mode? (Degrees)

Answer 13

no you shouldn't be doing much with degrees in calculus
it should be all about radians mostly

Answer 14

the calculator should be in radians

Answer 15

ok, I'll try and see. thanks for your help

Answer 16

It worked!!! thank you!!

So, I should now stay in Radians when there's always PI and change to degrees when specified otherwise, right?

Answer 17

stay in radians
i never seen a calculus class ever consider degrees

you had x approaches pi/2 earlier
you changed this to x approaches 90 deg
you change the "units" for a number while not changing the units for x

but I guess if you want to you could write
\[\lim_{x \rightarrow \frac{\pi}{2}} \frac{\cos(x)}{x-\frac{\pi}{2}} =\lim_{x \rightarrow 90^o} \frac{\cos(\frac{x \pi}{180^o})}{\frac{ x \pi}{180^o}-\frac{\pi}{2}}\]

Answer 18

ok thanks

Answer 19

but yeah I wouldn't do that
I wouldn't change radians to degrees ever in calculus