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Evaluate the limit: lim (x -> 0) (x^2)/(sin(x))
Evaluate the limit: lim (x -> 0) (x^2)/(sin(x))
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Practice Questions
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Q1
Evaluate the limit: lim (x -> 0) (x^2)/(sin(x))
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As x approaches 0, sin(x) approaches x, thus lim (x -> 0) (x^2)/(sin(x)) = 0.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate the limit: lim (x -> 0) (x^2)/(sin(x))
Solution:
As x approaches 0, sin(x) approaches x, thus lim (x -> 0) (x^2)/(sin(x)) = 0.
Steps: 6
Show Steps
Step 1: Understand the limit we want to evaluate: lim (x -> 0) (x^2)/(sin(x)).
Step 2: Recall that as x approaches 0, the value of sin(x) gets very close to x.
Step 3: Rewrite the limit using this knowledge: lim (x -> 0) (x^2)/(sin(x)) is similar to lim (x -> 0) (x^2)/x.
Step 4: Simplify (x^2)/x to get x, so now we have lim (x -> 0) x.
Step 5: As x approaches 0, the value of x also approaches 0.
Step 6: Therefore, the limit lim (x -> 0) (x^2)/(sin(x)) equals 0.
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