1) Suppose that a function f(x) is defined for all real values of x, except x...

1) Suppose that a function f(x) is defined for all real values of x, except x = x_o. Can anything be said about lim x → x 0 f ( x ) ?

Give reasons for your answer.
2) If x⁴ ≤ f(x) ≤ x² for x in [-1,1] and x² ≤ f(x) ≤ x⁴ for x < -1 and x > 1, at what points c do you automatically know lim x → c f ( x ) ? What can you say about the value of the limits at these points (x = +/-1) and at x = 0?

3) Explain why the following statement is true or false:
If g is continuous and increasing on its entire domain, then g(x₂) > g(x₁) when x₁ < x₂

Expert Solution

Colby Messinger answered 1 year ago

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Question

1) Suppose that a function f(x) is defined for all real values of x, except x...

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