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FROM CLASSROOM TO FAMILY
Attendance recorded. An absence followed up. A parent informed. Tools to connect the details of the school day.
Inside the platformApplication online / sign-in required02 / Understand
More than the answer. A way to get there. Try an excerpt of the public exercise, one clue at a time.
Explore the learning experienceAn excerpt of Understand’s public exercise, presented here. Your progress is not saved.
0? Careful: numerator and denominator both approach zero. That is an indeterminate form.
Set u = arctan t. Then t = tan u. As t approaches 0, what happens to u?
The fraction arctan t / t becomes u / tan u. You may recognise the limit of tan u / u.
arctan is continuous at 0 and arctan 0 = 0, so u approaches 0 with t. For t ≠ 0, arctan t / t = u / tan u.
Since tan u / u approaches 1, its reciprocal u / tan u also approaches 1. By composition:
limt → 0 arctan t / t = 1
One clue, then another. The answer comes with the reasoning.
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