1. Limits and Continuity

Limits and Continuity

On what intervals are the following functions continuous?

c. h(x) = x⁻²/³

Limits and Continuity

On what intervals are the following functions continuous?

a. ƒ(x) = tan x

Limits and Continuity

On what intervals are the following functions continuous?

b. g(x) = csc x

Limits and Continuity

On what intervals are the following functions continuous?

c. h(x) = cos x / x―π

Limits and Continuity

On what intervals are the following functions continuous?

b. g(x) = x³/⁴

Limits and Continuity

On what intervals are the following functions continuous?

d. k(x) = x⁻¹/⁶

Limits and Continuity

On what intervals are the following functions continuous?

d. k(x) = sin x / x

In Exercises 1–4, say whether the function graphed is continuous on [−1, 3]. If not, where does it fail to be continuous and why?

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In Exercises 1–4, say whether the function graphed is continuous on [−1, 3]. If not, where does it fail to be continuous and why?

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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.

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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.

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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.

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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 = 1/(|x| + 1) − x²/2

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

y = √(x⁴ +1)/(1 + sin² x)