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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)?
  • 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: We want to find out what happens to sin(x)/x as x gets closer to 0.
  • Step 4: Directly substituting x = 0 into sin(x)/x gives us 0/0, which is undefined. So we need another method.
  • Step 5: Use the squeeze theorem or known limit properties. It is a known fact that as x approaches 0, sin(x)/x approaches 1.
  • Step 6: Therefore, we conclude that lim(x->0) (sin(x)/x) = 1.
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