Explain every step are openShow that the subrests of the planeLet A CIR² be the open unit disk D, (0,0) with thepoint x₁ = (1,0) added, and let fit-IR₁ × → f(x)be the constant function f(x)=1.Show that limitfex) = 1.22.x → Xo

22.J Show that the subsests of the plane are open Let ACIR²2 be the open unit disk D, (0,0) with the point x = (1,0) added, and let fit-IR, x-f(x) be the constant function f(x) = 1. Show that limit fax) = 1. X-Xo

22.J Show that the subsests of the plane are open Let ACIR²2 be the open unit disk D, (0,0) with the point x = (1,0) added, and let fit-IR, x-f(x) be the constant function f(x) = 1. Show that limit fax) = 1. X-Xo

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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Question

Explain every step

are open
Show that the subrests of the plane
Let A CIR² be the open unit disk D, (0,0) with the
point x₁ = (1,0) added, and let fit-IR₁ × → f(x)
be the constant function f(x)=1.
Show that limit
fex) = 1.
22.
x → Xo

Expert Solution

Step 1

Note: First line of question is not mentioned that which subset need to show open. Therefore we will solve the next line onwards.

Given that $A \subset ℝ^{2}$ be the open unit disk $D (0, 0)$ with the point $x_{0} = (1, 0)$ is added to it.

The given function is $f : A \to ℝ$ be a constant function defined as $f (X) = 1$ for all $X \in A$ .

We know that if a function $f : A \to ℝ$ is defined, then the $\lim_{X \to X_{0}} f (X) = L$ , if for all $ε > 0$ , there exits $δ > 0$ such that $|f (X) - L| < ε$ , whenever $|X - X_{0}| < δ$ , whenever $X \in A$ .

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