Question: Calculate the limit: lim (x -> 0) (tan(3x)/x)
Options:
3
1
0
Infinity
Correct Answer: 3
Solution:
Using the standard limit lim (x -> 0) (tan(kx)/x) = k, we have k = 3, so the limit is 3.
Calculate the limit: lim (x -> 0) (tan(3x)/x)
Practice Questions
Q1
Calculate the limit: lim (x -> 0) (tan(3x)/x)
3
1
0
Infinity
Questions & Step-by-Step Solutions
Calculate the limit: lim (x -> 0) (tan(3x)/x)
Step 1: Identify the limit we want to calculate: lim (x -> 0) (tan(3x)/x).
Step 2: Recognize that this limit can be related to a standard limit form: lim (x -> 0) (tan(kx)/x) = k, where k is a constant.
Step 3: In our case, k is 3 because we have tan(3x).
Step 4: Apply the standard limit result: since k = 3, we find that lim (x -> 0) (tan(3x)/x) = 3.
Step 5: Conclude that the limit is 3.
Limit of a Function – Understanding how to evaluate the limit of a function as it approaches a specific value, particularly using known standard limits.
Trigonometric Limits – Applying the standard limit involving trigonometric functions, specifically the behavior of tan(kx) as x approaches 0.
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