01.07 Squeeze Theorem and Representations of Limits

Let f and g be functions defined as f(x)= x^2 − 2x + 4 and g(x) = 1/(x^2) + 2/5. If h(x) ≥ g(x) and h(x) ≤ f(x) for all values of x, what is lim x→0 h(x)?

D. Cannot be determined based on the information

If f(x) = x^2 cos (1/(x^2)), which inequality can be used with the Squeeze Theorem to find lim x→0 f(x)?

A. -x^2 ≤ f(x) ≤ x^2

Let k(x) be a piecewise defined function so that (sinx)/x if x ≠ 0 k(x) = { } 0 if x = 0 The function h(x) is given by the graph below. Which of the following equals lim x→0 (k(x) - h(x))/k(x)?

A. 0

Let f, g, and h be functions defined as f(x) = xsin(1/(x^2)), g(x) = x^2 sin 1/x, and h(x) = (sinx)/x. Which of the following inequalities can be used with the Squeeze Theorem to find the limit of the function as x approaches 0? I. -|x| ≤ f(x) ≤ |x| II. -x^2 ≤ g(x) ≤ x^2 III. -x ≤ h(x) ≤ x

A. I and II

The table represents f(x) and the graph represents function g(x). Which of the following could represent the value of lim x→1 [2f(x) + g(x)^2]? x [0.95, 0.99, 1, 1.01, 1.05] f(x) [0.875, 0.998, 1, 1.002, 1.102]

C. 3