Question

Evaluate\[\lim_{x \rightarrow \infty} \text{Arcsin}(\frac{x+2}{x+1})\]

Answer 1

arcsin(1)

Answer 2

pi/2?

Answer 3

or we can't take lim inside??

Answer 4

we can

Answer 5

so what is it?

Answer 6

pi/2+2npi

Answer 7

@mukushla...i got pi/2. i took tke limit inside; there i divided each element by the variable with the highest degree which is obviously x. i had limit as x app infinity (1+2/y)/(1+1/y) where y is a very large number. 2/y and 1/y then approach 0 rendering everything in the bracket all equals 1. i then took the arcsine of 1

Answer 8

u guys still missing something

Answer 9

x cannot take the value of infinity,arcsin is bounded.

Answer 10

so limit does not exist

Answer 11

u sure we can take lim inside?

Answer 12

yes like this\[\lim_{x \rightarrow \infty} \text{Arcsin}(\frac{x}{x+1})=\text{Arcsin} (1)=\frac{\pi}{2}\]

Answer 13

hey man u lost me...what did u do to whats inside the bracket?