limit (x csc x) is?
as x approaches zero

Question

limit (x csc x) is?
as x approaches zero

amistre64 · Answer

cscx = 1/sinx

amistre64 · Answer

$$\lim_{x\to~0}\frac{sin~x}{x}=1$$
therefore, what do you think the limit would be of
$$\lim_{x\to~0}\frac{x}{sin~x}$$

anonymous · Answer

thank you. but the answer you gave is not one of the choices

amistre64 · Answer

we arent spose to give direct answers, only guidance

anonymous · Answer

okay. thank you.

anonymous · Answer

do i plug in the zero in both of the x?

amistre64 · Answer

no, you should "know" that sin(x)/x has a limit of 1; and that x csc(x) is just x/sin(x)  and compare the results

amistre64 · Answer

there is something to do with a squeeze thrm which i never really can implement, or a Lhopital

anonymous · Answer

lol proving what amistre said would require squeeze therorem and that's a pain lol

anonymous · Answer

theorem*
we had to do that on our first test

amistre64 · Answer

:)

anonymous · Answer

squeeze theorem isn't hard, just almost unnecessary as most of what it proves in many cases that we use it in can be considered kind of like rules.

anonymous · Answer

so sin x/sinx = 1 is a rule?

anonymous · Answer

well anything over itself is 1

anonymous · Answer

i mean x/sinx. sorry

amistre64 · Answer

rule to memorize
$$\lim_{x\to~0}\frac{sin~x}{x}=1$$

anonymous · Answer

That is more like a law lol.

anonymous · Answer

(the anything over itself bit)

amistre64 · Answer

0/0 aint 1 ;)

anonymous · Answer

the one exception lol

anonymous · Answer

Our professors don't really treat zero as a number sometimes lol. Anything over 0 is undefined

anonymous · Answer

do you guys know increasing/decreasing using the first derivatives of a equation and concavity using 2nd deriv.?

anonymous · Answer

and a limit with 0 as the denominator (with the exception of 0 as the numerator as well, which would entail L'Hopital's rule) is DNE

anonymous · Answer

yes

anonymous · Answer

do you have a specific question in mind about those, such as drawing a graph?

anonymous · Answer

so lets say in a func the 1st deriv is greater than 0 for all x but the 2nd deriv is less than 0 for all x? how would  a graph of that look like? and can you explain the reasoning behind you ans.

anonymous · Answer

that means that it is positive, increasing, but concave down so something like this|dw:1354141662047:dw| forgive my poor mouse skills