Question #15374

(a) Show that the function
g(x) = (3 + sin (1/x-2)/ (1 + x^2)
is bounded. This means to find real numbers m, M E R such that m ≤ g(x) ≤ M for
all x E R (and to show that these inequalities are satisfied!).
(b) Explain why the function
f(x) = { [x-2] [3 + sin (1/x-2)/ (1 + x^2)] if x ≠ 2,
{0, if x = 2
is continuous at all x ≠ 2
(c) Show that the function f(x) in Part (b) is continuous at x = 2. [Hint: Use
Part (a) and the Squeeze Theorem.]

Expert's answer

Unfortunately, your question requires a lot of work and cannot be done for free.

Submit it with all requirements as an assignment to our control panel and we'll assist you.

Submit it with all requirements as an assignment to our control panel and we'll assist you.

## Comments

## Leave a comment