# Answer on Calculus Question for hsd

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.]

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.

Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

## Leave a comment