Question: Find the limit: lim (x -> 0) (sin(5x)/x)
Options:
0
5
1
Infinity
Correct Answer: 5
Solution:
Using the limit property, lim (x -> 0) (sin(kx)/x) = k. Here, k = 5, so the limit is 5.
Find the limit: lim (x -> 0) (sin(5x)/x)
Practice Questions
Q1
Find the limit: lim (x -> 0) (sin(5x)/x)
0
5
1
Infinity
Questions & Step-by-Step Solutions
Find the limit: lim (x -> 0) (sin(5x)/x)
Step 1: Identify the limit we want to find: lim (x -> 0) (sin(5x)/x).
Step 2: Recognize that this limit can be solved using a known limit property: lim (x -> 0) (sin(kx)/x) = k, where k is a constant.
Step 3: In our case, k is 5 because we have sin(5x).
Step 4: Apply the limit property: since k = 5, we find that lim (x -> 0) (sin(5x)/x) = 5.
Step 5: Conclude that the limit is 5.
Limit of a Function – Understanding how to evaluate limits, particularly those involving trigonometric functions and their behavior as they approach zero.
Sine Limit Property – Applying the specific limit property that states lim (x -> 0) (sin(kx)/x) = k, which is crucial for solving this type of limit problem.
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