Question

lim x --> 0 , ( 1 + (cotx)^2) /( cscx )^3

Answer 1

use your trig

Answer 2

could i use l'hopital rule

Answer 3

i would try simplifying the expression first

Answer 4

(2cotx (-(cscx)^2) )/ 3 cscx (-(cscxcotx) = 2/3, but the simplified one is equal to something else?

Answer 5

( 1 + (cotx)^2) /( cscx )^3 = (cscx)^2 / (cscx)^3 = 1/cscx = sinx

Answer 6

so therefore i cannot use l'hopitals rule and must simplify instead?

Answer 7

you need to check if the expression is in indeterminate form before using l'hopitals

Answer 8

i got 1 +infinity over +/-infinity is that allowed, so infinity/infinity form

Answer 9

trying lhopital here is just ridiculous here as it simplifies nicely without lhopital

Answer 10

why is the answers different?

Answer 11

yeah im thinking the same, it should not fail if it is indeterminate

Answer 12

you only can use
lim sinx/x =1 or anything derived from it

Answer 13

so this equation isn't derived from sinx/x? which is the reason it doesn't work

Answer 14

well tricky a bit it would be something solvable lets say m
lim m . x =0

Answer 15

limit of a equation "m" as x approaches 0?

Answer 16

i just dont wanna complicated u lol
why dont u work on it simply and expand all terms ?

Answer 17

limit 1/csc x is not infinity :O

Answer 18

limit of (cscx)^3 is not infinity as x->0

Answer 19

? plus or minus infinity

Answer 20

just work simply