Find the value of the limit: lim (x -> 0) (sin x)/x.
Practice Questions
Q1
Find the value of the limit: lim (x -> 0) (sin x)/x.
0
1
∞
undefined
Questions & Step-by-Step Solutions
Find the value of the limit: lim (x -> 0) (sin x)/x.
Correct Answer: 1
Step 1: Understand the limit notation. We want to find what happens to the value of (sin x)/x as x gets very close to 0.
Step 2: Recognize that directly substituting x = 0 into (sin x)/x gives us 0/0, which is undefined.
Step 3: Use a known limit result: lim (x -> 0) (sin x)/x = 1. This is a standard limit in calculus.
Step 4: Conclude that as x approaches 0, the value of (sin x)/x approaches 1.
Limit of a Function – Understanding how to evaluate the limit of a function as it approaches a specific value, particularly using the Squeeze Theorem or L'Hôpital's Rule.
Trigonometric Limits – Recognizing the standard limit involving sine and its relationship to the unit circle and small angle approximations.
