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Evaluate the limit: lim (x -> 0) (tan(x)/x) (2023)

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Question: Evaluate the limit: lim (x -> 0) (tan(x)/x) (2023)

Options:

  1. 0
  2. 1
  3. ∞
  4. Undefined

Correct Answer: 1

Exam Year: 2023

Solution: 

Using the limit property lim (x -> 0) (tan(x)/x) = 1, we find that the limit is 1.

Evaluate the limit: lim (x -> 0) (tan(x)/x) (2023)

Practice Questions

Q1
Evaluate the limit: lim (x -> 0) (tan(x)/x) (2023)
  1. 0
  2. 1
  3. ∞
  4. Undefined

Questions & Step-by-Step Solutions

Evaluate the limit: lim (x -> 0) (tan(x)/x) (2023)
  • Step 1: Understand the limit we want to evaluate: lim (x -> 0) (tan(x)/x).
  • Step 2: Recall a known limit property: lim (x -> 0) (tan(x)/x) = 1.
  • Step 3: Since we know that lim (x -> 0) (tan(x)/x) = 1, we can substitute this into our limit.
  • Step 4: Multiply the result by 2023: 1 * 2023 = 2023.
  • Step 5: Therefore, the final answer is 2023.
  • Limit Evaluation – Understanding how to evaluate limits, particularly using known limit properties.
  • Trigonometric Limits – Applying specific limits involving trigonometric functions, such as tan(x) as x approaches 0.
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