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What is the value of the limit lim(x→0) (sin(x)/x)?
What is the value of the limit lim(x→0) (sin(x)/x)?
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Q1
What is the value of the limit lim(x→0) (sin(x)/x)?
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The limit lim(x→0) (sin(x)/x) = 1.
Questions & Step-by-step Solutions
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Q: What is the value of the limit lim(x→0) (sin(x)/x)?
Solution:
The limit lim(x→0) (sin(x)/x) = 1.
Steps: 6
Show Steps
Step 1: Understand what a limit is. A limit tells us what value a function approaches as the input gets closer to a certain point.
Step 2: Identify the function we are looking at, which is sin(x)/x.
Step 3: Notice that we want to find the limit as x approaches 0.
Step 4: Recognize that directly substituting x = 0 into sin(x)/x gives us 0/0, which is undefined.
Step 5: Use a known mathematical fact or rule that states lim(x→0) (sin(x)/x) = 1.
Step 6: Conclude that the value of the limit is 1.
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