Question

Find the limit:

Answer 1

The limit of (d) of the complex number
\[Z = \frac{ 1 }{ sind } + \frac{ 1 }{ cosd } i \]
d -> pi/2
[No l'hopital]

Answer 2

Are you thinking guys or the question doesn't show ?

Answer 3

I was thinking, but now it seems you can just test the left and right hand limits and you sill see that the limit diverges

Answer 4

Clarify a bit

Answer 5

\[\large \lim_{d\to\pi/2^+}\frac1{\sin x}+\frac1{\cos x}i\\\large\lim_{d\to\pi/2^-}\frac1{\sin x}+\frac1{\cos x}i\]

Answer 6

What is x ? and I am still confused.

Answer 7

a typo, sorry\[\large \lim_{d\to\pi/2^+}\frac1{\sin d}+\frac1{\cos d}i\\\large\lim_{d\to\pi/2^-}\frac1{\sin d}+\frac1{\cos d}i\]

Answer 8

do you know how to take a right-handed limit?\[\large \lim_{d\to\pi/2^+}\frac1{\sin d}+\frac1{\cos d}i\]

Answer 9

Generally , I can. But in this one especially I can't.

Answer 10

what is the limit of sinx as x approaches pi/2 from the positive side?

Answer 11

sin(pi/2) = 1

Answer 12

sinx/x if x approaches 0 Ops !

Answer 13

sorry?

Answer 14

Hmmm , seems like I am lost , aren't I ?

Answer 15

perhaps lol
do you know what a one-sided limit is?

Answer 16

Yeah, It's when a function approaches a point from right or left ( higher and lower values).

Answer 17

If that function has different left and right sided limits then It's limit doesn't exist.

Answer 18

Am I right or still lost ?

Answer 19

you are right, sorry i was distracted

Answer 20

so as x approaches pi/2 from the right, what value does sinx have? what about cosx?

Answer 21

You got the derivative ? " L'hopital rule" right ?

Answer 22

you don't want to use l'hospital, right?

Answer 23

Yep, written up !

Answer 24

I don't want "L'hospital rule" as It's higher than my grade , and each time I ask for limit they use it.

Answer 25

here is a unit circle

Answer 26

as d approaches pi/2 from the right...is sind positive or negative?