Exercises 5–10 refer to the function

f(x) = { x² − 1, −1 ≤ x < 0

2x, 0 < x < 1

1, x = 1

−2x + 4, 1 < x < 2

0, 2 < x < 3

graphed in the accompanying figure.

<IMAGE>

b. Does lim x → −1⁺ f (x) exist?

Exercises 5–10 refer to the function

f(x) = { x² − 1, −1 ≤ x < 0

2x, 0 < x < 1

1, x = 1

−2x + 4, 1 < x < 2

0, 2 < x < 3

graphed in the accompanying figure.

<IMAGE>

a. Does f (1) exist?

Exercises 5–10 refer to the function

f(x) = { x² − 1, −1 ≤ x < 0

2x, 0 < x < 1

1, x = 1

−2x + 4, 1 < x < 2

0, 2 < x < 3

graphed in the accompanying figure.

<IMAGE>

At what values of x is f continuous?

At what points are the functions in Exercises 13–30 continuous?

y = 1/(x – 2) – 3x

At what points are the functions in Exercises 13–30 continuous?

y = √(x⁴ +1)/(1 + sin² x)

At what points are the functions in Exercises 13–30 continuous?

y = (2x – 1)¹/³

At what points are the functions in Exercises 13–30 continuous?

f(x) = { (x³ − 8)/(x² − 4), x ≠ 2, x ≠ −2

3, x = 2

4, x = −2

Find the limits in Exercises 31–40. Are the functions continuous at the point being approached?

lim t → 0 sin (π/2 cos (tan t))