Limit of A Function : a^[f(x)]

f(x) is a continuous function.

Limit of sin(x)/x and tan(x)/x

Before you see this post,

see

A Property of Limit of A Function : f(x)/g(x),

Trigonometric Function : Sine, Cosine and Tangent,

Graph of Trigonometric Function : Sine, Cosine and Tangent

and

Radian

First, Let's divide the formula by sinθ.

There is a result.

Second, Let's divide the formula by tanθ. 

There is a result.

A Property of Limit of A Function : log_r [f(x)]

f(x) is a continuous function.

δ=δ0

e ( mathematical constant )

Before you see this post,

see

A Property of Limit of A Function : f(x)g(x)

and

A Property of Limit of A Function : log(r) [f(x)]

A Property of Limit of A Function : f(x)/g(x)

Before you see this post,

see

A Property of Limit of A Function : f(x)g(x)

f(x) is a continuous function.

let me show you that a property of limit of a function : 1/f(x).

δ=δ0

Use property of limit of a function : f(x)g(x) like the picture below.

Result will be showed like the picture above.

Continuous Function by ε,δ

Definition of continuous function by epsilon-delta (ε,δ) and its conditions

correction : lim [x->p] f(p) -> lim [x->p] f(x) at no. 3 on a picture above.

Limit of A Function : f(g(x))

f(x) and g(x) are continuous functions.

Sandwich Theorem

f(x), g(x) and h(x) are continuous functions.

A Property of Limit of A Function : n-th root of f (x)

Before you see this post,

See

A Property of Limit of A Function : {f(x)}^n

f(x) and n-th root of f(x) are continuous functions.

n ∈ ℕ (natural number )

A Property of Limit of A Function : {f(x)}^n

Before you see this post,

See

A Property of Limit of A Function : f(x)g(x)

f(x) and {f(x)}^n are continuous functions.

n ∈ ℕ (natural number )

A Property of Limit of A Function : cf(x)

f(x) is a continuous function.

A Property of Limit of A Function : constant

Uniqueness of Limit of A Function

f(x) is a continuous function

A Property of Limit of A Function : f(x)g(x)

Before you see this post,

See 

A Property of Limit of A Function : constant

A Property of Limit of A Function : cf(x)

A Property of Limit of A Function : f(x)+g(x)

f(x) and g(x) are continuous functions.

A Property of Limit of A Function : f(x)+g(x)

f(x) and g(x) are a continuous functions.

Epsilon-Delta Definition of Limit

For all ε, there is a δ in real number like picture above.

Let p be a limit of subset D.

Then, the function f(x) has a limit C at p.