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What is the value of the limit lim(x→0) (sin(x)/x)?

Practice Questions

Q1
What is the value of the limit lim(x→0) (sin(x)/x)?
  1. 0
  2. 1
  3. ∞
  4. undefined

Questions & Step-by-Step Solutions

What is the value of the limit lim(x→0) (sin(x)/x)?
Correct Answer: 1
  • 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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