GATE CE 2019 Set 2 — Question 13
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Engineering Mathematics → Calculus → Limits & Continuity
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Question
The following inequality is true for all close to 0.What is the value of ?
Correct answer
(D) 2
Solution
Using the Squeeze Theorem (also known as the Sandwich Theorem), if for all in an interval around (except possibly at ), and , then .Here, and .
As :
Since both the lower and upper bounds approach 2 as approaches 0, the limit of the middle function must also be 2.
.
As :
Since both the lower and upper bounds approach 2 as approaches 0, the limit of the middle function must also be 2.
.
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