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Find the value of the limit: lim (x -> 0) (sin x)/x.
Find the value of the limit: lim (x -> 0) (sin x)/x.
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Practice Questions
1 question
Q1
Find the value of the limit: lim (x -> 0) (sin x)/x.
0
1
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undefined
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The limit is 1.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the value of the limit: lim (x -> 0) (sin x)/x.
Solution:
The limit is 1.
Steps: 4
Show Steps
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.
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