- #1

ktpr2

- 192

- 0

[tex]g(x) = (sin 5x)/x[/tex]

[tex]h(x) = x^2+5[/tex]

I'm trying to find the limit of g(x) as x --> 0

I know that f(x) and h(x) are less than and greater than, respectively, than g(x) but I am unsure how to prove that w/o abusing the concept of infinity. How would I prove this so that i can show that

[tex]f(x)\leqq g(x) \leqq h(x)[/tex]

and use the squeeze theorem to show that the limit as x --> 0 for g(x) = 5 because it's also 5 for f(x) and h(x)? Alternatively, I'm sure, is there a better way to go about this?