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δ=?

2)Use the provided graph offto discover a numberδsuch thatif

http://imgur.com/qIpDK9r

Step 1:

(1)

The duty is

.

You are watching: Use the given graph of f(x) = x to find a number δ such that if |x − 4| < δ then x − 2 < 0.4.

Find

such that
whenever
.

Definition of limit:

Let

be a role defined ~ above an open interval containing
and also let
be a genuine number.

The declare

means that for every

, there exists a
such the
, climate
.

Step 2:

whenever
.

We need to create a connection between

and
.

Consider

.

Solve the inequality.

Subtract

from each side.

Since

,

Compare the above with

, climate
.

Solution:

.

Step 1:

(2)

Find

such that
whenever
.

Definition of limit:

Let

be a duty defined top top an open interval containing
and let
be a actual number.

The statement

means that for each

, over there exists a
such that
, then
.

Step 2:

at any time
.

Consider

.

Observe the graph:

Compare

and
.

See more: What Is 36 Degrees Celsius In Fahrenheit ), What Is 36 Degrees Celsius In Fahrenheit

Lower value:

Upper value:

The worths of

room 0.1 and also 0.3

Solution:

The values of

are 0.1 and also 0.3.