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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.