Show that the following limit is true 1 lim 240 First note

Last updated: 9/15/2023

Show that the following limit is true 1 lim 240 First note that we cannot use 1 lim sin lim 2 0 I 2 0 sin I sin 1 lim sin I 0 1 because the limit as a approaches 0 of sin does not exist see this example Instead we a I 1 the Squeeze Theorem and so we need to find a function f smaller than g x x sin function h bigger than g such that both f x and h x approach 0 To do this we use our knowledge of the sine function Because the sine of any number lies between and we can write x 1 x and Any inequality remains true when multiplied by a positive number We know that a 0 for all a and so multiplying each side of inequalities of x we get 1