Question

use the squeeze thermo to determine ; lim x- infinity 3 - sin ( e x) / spuare x ^ 2 + 2

Answer 1

Is your limit
\[
\lim_{x\to \infty} \frac { 3 -\sin( e^x)}{\sqrt{x^2+2}}
\]

Answer 2

\[
0\le \left | \frac { 3 -\sin( e^x)}{\sqrt{x^2+2}} \right|\le \left | \frac { 3}{\sqrt{x^2+2}} \right| + \left | \frac { 1}{\sqrt{x^2+2}} \right|
\]
Can you argue to finish it?

Answer 3

The RHS goes to zero so the quantity in between goes to zero by the squeeze theroem

Answer 4

If the absolute value of a quantity goes to zero, the quantity itself does the same.

Answer 5

thanks a lot i understand it must i show througher calculations ?

Answer 6

sorry i dont understand the squeezze theroem it counts 15 marks in my assignment

Answer 7

The squeeze theorem says if
\[
f(x)\le g(x) \le h(x)\\ if \\
\lim_{x\to a} f(x)=\lim_{x\to a}h(x)=L\\then\\
\lim_{x\to a} g(x)=L
\]