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Evaluate the limit: lim (x -> 0) (sin(5x)/x)
Evaluate the limit: lim (x -> 0) (sin(5x)/x)
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Practice Questions
1 question
Q1
Evaluate the limit: lim (x -> 0) (sin(5x)/x)
0
5
1
Infinity
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Using the standard limit lim (x -> 0) (sin(x)/x) = 1, we have lim (x -> 0) (sin(5x)/x) = 5 * lim (x -> 0) (sin(5x)/(5x)) = 5 * 1 = 5.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate the limit: lim (x -> 0) (sin(5x)/x)
Solution:
Using the standard limit lim (x -> 0) (sin(x)/x) = 1, we have lim (x -> 0) (sin(5x)/x) = 5 * lim (x -> 0) (sin(5x)/(5x)) = 5 * 1 = 5.
Steps: 7
Show Steps
Step 1: Identify the limit we want to evaluate: lim (x -> 0) (sin(5x)/x).
Step 2: Recall the standard limit: lim (x -> 0) (sin(x)/x) = 1.
Step 3: Notice that we can rewrite sin(5x) in terms of sin(5x)/(5x).
Step 4: Rewrite the limit: lim (x -> 0) (sin(5x)/x) = lim (x -> 0) (sin(5x)/(5x)) * 5.
Step 5: Now, we can apply the standard limit: lim (x -> 0) (sin(5x)/(5x)) = 1.
Step 6: Multiply the result by 5: 5 * 1 = 5.
Step 7: Conclude that the limit is 5.
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