I really need help on this sketch the graph of f. Then identify thelim f(x) exists.X-Cx².35. f(x)=8 - 2x,4,x ≤ 22 < x < 4x ≥ 4

Answered: sketch the graph of f. Then identify…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

I really need help on this

sketch the graph of f. Then identify the
lim f(x) exists.
X-C
x².
35. f(x)=8 - 2x,
4,
x ≤ 2
2 < x < 4
x ≥ 4

Expert Solution

Step 1

Concept:

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.

When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.

This could be expressed as

$\lim_{x \to a} f (x) = A^{+}$

When a variable approaches its limit from the left, the function's left-hand limit is the value that approaches.

This could be expressed as

$\lim_{x \to a} f (x) = A^{-}$

If and only if the left-hand limit and the right-hand limit are equal, then a function has a limit.

$\lim_{x \to a^{-}} f (x) = \lim_{x \to a^{+}} f (x) = L$