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Question 1 of 9

+1.0 Marks

1. lim (x→0) (sin 2x) / x =

A 0 B 1 C 1/2 D 2 E does not exist

Question 2 of 9

+1.0 Marks

7. At what value of x does the function f(x) = (x + 1)² / (x² - 1) have a removable discontinuity?

A -3 B 3 C 2 D -1 E 1

Question 3 of 9

+1.0 Marks

9. For the function f(x) whose graph is shown, which statement is false?

A lim (x→1) f(x) = 1 B lim (x→2⁻) f(x) = 2 C lim (x→0⁺) f(x) = lim (x→0⁻) f(x) D lim (x→-1) f(x) = 2 E lim (x→-1⁺) f(x) = 2

Question 4 of 9

+1.0 Marks

6. Find the value of the limit: lim (x→2) (x³ - 8) / (x - 2)

A 8 B 4 C 2 D 12 E 6

Question 5 of 9

+1.0 Marks

8. Suppose g is a function defined on the interval [0, 5] such that lim (x→2) g(x) = -1, find lim (x→2) [g(x)]³

A 8 B 1/8 C -1 D 1/3 E does not exist

Question 6 of 9

+1.0 Marks

2. The graph of y = (2x² + 2x + 3) / (4x² - 4x) has

A a horizontal asymptote at y = 1/2 but no vertical asymptotes B no horizontal asymptotes but two vertical asymptotes, at x = 0 and x = 1 C a horizontal asymptote at y = 1/2 and two vertical asymptotes, at x = 0 and x = 1 D a horizontal asymptote at x = 2 but no vertical asymptotes E a horizontal asymptote at y = 1/2 and two vertical asymptotes at x = 1 and x = -1

Question 7 of 9

+1.0 Marks

4. Find lim (x→7⁻) |8x - 56| / (7 - x)

A 8 B -1 C 1 D -8 E does not exist

Question 8 of 9

+1.0 Marks

3. Given that lim (x→1) (2x + 1) = 3, find δ such that |(2x + 1) - 3| ≤ 0.01 whenever 0 < |x - 1| ≤ δ.

A 3 B 0.05 C 0.005 D 0.03 E 0.02

Question 9 of 9

+1.0 Marks

5. Find lim (x→2) 1 / (x - 2)²

A ∞ B -∞ C 0 D 1/4 E does not exist

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