Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. p(v) = 5/11v² + 5, a = 1 lim p(v) v-1 lim 5/11v2 + 5 v-1 Jim V11v2 + 5 by the ---Select--- -Select--- %3D lim (11v2 + 5 v-1 Sum Law = 5 by the Difference Law Constant Multiple Law Product Law Quotient Law lim (11v + lim 5 V-1 = 5 by the v-1 Power Law = 5/ 11 lim (v2 v-1 + lim 5 v-1 by the Root Law Direct Substitution Property = 5/11· (1) + 5 by the --Select--- Find p(1). p(1) = Thus, by the definition of continuity, p is continuous at a = 1.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 38E
Question
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
p(v)
= 5V 11v2 + 5,
a = 1
lim p(v)
v-1
lim 5/11v2 +
v-1
5 lim v11v2 + 5
by the ---Select---
---Select---
V-1
lim (11v2 + 5
Sum Law
Difference Law
by the
V-1
Constant Multiple Law
lim (11v2) + lim 5
by the Product Law
Quotient Law
V-1
V-1
Power Law
11 lim
v-1
v2) + lim 5
V→1
Root Law
= 5
by the
Direct Substitution Property
= 5V11 · (1) + 5
by the ---Select---
Find p(1).
p(1) =
Thus, by the definition of continuity, p is continuous at a = 1.
Transcribed Image Text:Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. p(v) = 5V 11v2 + 5, a = 1 lim p(v) v-1 lim 5/11v2 + v-1 5 lim v11v2 + 5 by the ---Select--- ---Select--- V-1 lim (11v2 + 5 Sum Law Difference Law by the V-1 Constant Multiple Law lim (11v2) + lim 5 by the Product Law Quotient Law V-1 V-1 Power Law 11 lim v-1 v2) + lim 5 V→1 Root Law = 5 by the Direct Substitution Property = 5V11 · (1) + 5 by the ---Select--- Find p(1). p(1) = Thus, by the definition of continuity, p is continuous at a = 1.
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