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Find the limit: lim(x->0) (tan(3x)/x)

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Question: Find the limit: lim(x->0) (tan(3x)/x)

Options:

  1. 3
  2. 0
  3. 1
  4. Infinity

Correct Answer: 3

Solution: 

Using the limit property, lim(x->0) (tan(kx)/x) = k. Here, k = 3, so the limit is 3.

Find the limit: lim(x->0) (tan(3x)/x)

Practice Questions

Q1
Find the limit: lim(x->0) (tan(3x)/x)
  1. 3
  2. 0
  3. 1
  4. Infinity

Questions & Step-by-Step Solutions

Find the limit: lim(x->0) (tan(3x)/x)
  • Step 1: Identify the limit we need to find: lim(x->0) (tan(3x)/x).
  • Step 2: Recognize that this limit can be simplified using a known limit property.
  • Step 3: Recall the limit property: lim(x->0) (tan(kx)/x) = k, where k is a constant.
  • Step 4: In our case, k is 3 because we have tan(3x).
  • Step 5: Apply the limit property: since k = 3, we find that lim(x->0) (tan(3x)/x) = 3.
  • Step 6: Conclude that the limit is 3.
  • Limit of a Function – Understanding how to evaluate limits as a variable approaches a specific value, particularly using known limit properties.
  • Trigonometric Limits – Applying the limit property for trigonometric functions, specifically the behavior of tan(kx) as x approaches 0.
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