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Calculate the limit: lim (x -> 0) (tan(5x)/x) (2022)

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Question: Calculate the limit: lim (x -> 0) (tan(5x)/x) (2022)

Options:

  1. 0
  2. 1
  3. 5
  4. Undefined

Correct Answer: 5

Exam Year: 2022

Solution: 

Using the limit property lim (x -> 0) (tan(kx)/x) = k, we have lim (x -> 0) (tan(5x)/x) = 5.

Calculate the limit: lim (x -> 0) (tan(5x)/x) (2022)

Practice Questions

Q1
Calculate the limit: lim (x -> 0) (tan(5x)/x) (2022)
  1. 0
  2. 1
  3. 5
  4. Undefined

Questions & Step-by-Step Solutions

Calculate the limit: lim (x -> 0) (tan(5x)/x) (2022)
  • Step 1: Understand the limit we want to calculate: lim (x -> 0) (tan(5x)/x).
  • Step 2: Recognize that we can use a special limit property: lim (x -> 0) (tan(kx)/x) = k, where k is a constant.
  • Step 3: In our case, k is 5 because we have tan(5x).
  • Step 4: Apply the limit property: lim (x -> 0) (tan(5x)/x) = 5.
  • Step 5: Therefore, the limit we calculated is 5.
  • Limit of a Function – Understanding how to evaluate limits, particularly as they approach zero, and applying known limit properties.
  • Trigonometric Limits – Applying the specific limit property of the tangent function as it approaches zero.
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