Concept explainers
If 2x ≤ g(x) ≤ x4 – x2 + 2 for all x, evaluate
To evaluate: The limit value of the function
Answer to Problem 30E
The limit value of the function
Explanation of Solution
Given:
The inequality is,
Limit Laws:
Suppose that c is a constant and the limits
Limit law 1:
Limit law 2:
Limit law 3:
Limit law 7:
Limit law 8:
Limit law 9:
Theorem used: The Squeeze Theorem
“If
Calculation:
Apply the Squeeze Theorem and obtain a function f smaller than
The given inequality becomes,
When the limit x approaches to 1, the inequality becomes,
Let
Obtain the limit value of as x approaches 1 of the function
Obtain the limit value of as x approaches 1 of the function
If
Therefore,
Thus, the limit value of the function
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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