Continuity

Courses

About SOWISO

Contact

Unlock

Courses

About SOWISO

Contact

Unlock

unit
abc
abc
abc
vector
logic
function
standard

α

β

δ

γ

ϵ

ζ

η

θ

ι

κ

λ

μ

ν

ξ

ο

π

ρ

σ

τ

υ

φ

χ

ψ

ω

Δ

Γ

Θ

Λ

Ξ

Σ

Φ

Ψ

Ω

abc

↵

(

)

C

↑

←

↓

→

x

y

#x#

unit
abc
abc
abc
vector
logic
function
standard

Q

W

E

R

T

Y

U

I

O

P

A

S

D

F

G

H

J

K

L

shift

Z

X

C

V

B

N

M

greek

↵

(

)

C

↑

←

↓

→

x

y

#x#

unit
abc
abc
abc
vector
logic
function
standard

q

w

e

r

t

y

u

i

o

p

a

s

d

f

g

h

j

k

l

shift

z

x

c

v

b

n

m

greek

↵

(

)

C

↑

←

↓

→

x

y

#x#

unit
abc
abc
abc
vector
logic
function
standard

7

8

9

+

4

5

6

−

1

2

3

÷

.

0

=

×∗×

√

a

{......

[

,

]

,

∞

{}

det

(m×n)

∙

↵

(

)

C

↑

←

↓

→

x

y

#x#

unit
abc
abc
abc
vector
logic
function
standard

p

∧

⊥

φ

∀

>

=

⊢

N

∅

∪

⊂

q

∨

⊤

ψ

∃

<

≠

⊨

Z

∈

∩

⊆

r

→

□

χ

P

≥

∖

Q

∉

⇒

⊬

⊃

¬

↔

◇

⧆

R

≤

⊭

≡

{}

R

⇔

⊇

↵

(

)

C

↑

←

↓

→

x

y

a

#x#

unit
abc
abc
abc
vector
logic
function
standard

7

8

9

+

4

5

6

−

1

2

3

÷

.

0

=

×∗×

√

a

>

log

sin

[

,

]

<

ln

cos

lim

∞

[

,

)

≥

|

|

tan

e

,

(

,

]

≤

!

π

i

a

{......

(

,

)

↵

(

)

C

↑

←

↓

→

x

y

#x#

unit
abc
abc
abc
vector
logic
function
standard

7

8

9

+

4

5

6

−

1

2

3

÷

.

0

=

×∗×

√

a

>

log

sin

∧

∨

<

ln

cos

all

none

≥

|

|

tan

e

≤

!

π

°

↵

(

)

C

↑

←

↓

→

x

y

#x#

unit
abc
abc
abc
vector
logic
function
standard

C

J

N

Pa

W

A

°C

K

g

l

m

V

s

min

h

d

w

mo

y

acre

yd

ft

mile

mol

pt

bar

y

z

a

f

p

n

μ

m

c

d

da

h

k

M

G

T

P

E

Z

Y

unit

↵

(

)

C

↑

←

↓

→

x

y

#x#

unit
abc
abc
abc
vector
logic
function
standard

7

8

9

+

4

5

6

−

1

2

3

÷

.

0

=

×∗×

√

a

>

log

sin

∧

∨

<

ln

cos

all

none

≥

|

|

tan

e

≤

!

π

°

↵

(

)

C

↑

←

↓

→

x

y

#x#

1

2

3

4

5

6

Functions: Introduction to functions

Continuity

Which of the following functions on the real numbers are discontinuous?

The Heaviside function #\displaystyle \theta(x)=\begin{cases}0&x\lt 0\\1&x\geq0\end{cases}#

The sign function (or the signum) #\textrm{sgn}(x)=\begin{cases}-1&x\lt 0\\0&x=0\\1&x\gt0\end{cases}#

The absolute value function #\displaystyle |x|=\begin{cases}-x&x\lt 0\\ x&x\ge0\end{cases}#

The square root of the absolute value function # \sqrt{|x|}#

Unlock full access unlock

unlock

Teacher access

Request a demo account. We will help you get started with our digital learning environment.

Create demo account

Student access

Is your university not a partner? Get access to our courses via Pass Your Math independent of your university. See pricing and more.
Or visit omptest.org if jou are taking an OMPT exam.

More info

About us ⋅ Help ⋅ Privacy ⋅ Terms and conditions
Copyright © 2023 SOWISO