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Dania Mueller

Dania Mueller

Answered question

2022-06-17

Evaluate the limit lim x 2 cos π x x 2

Answer & Explanation

Marlee Guerra

Marlee Guerra

Beginner2022-06-18Added 25 answers

We have
L = lim x 2 cos π x x 2 = lim x 2 sin ( π 2 π x ) π 2 π x × π 2 π x x 2
We let t = π 2 π x . Then, we get,
L = lim t 0 sin t t × t t π 2 t 2
L = ?
Hope you can take it from here.
Yahir Crane

Yahir Crane

Beginner2022-06-19Added 9 answers

take ϕ ( x ) = cos ( π x ) then, since cos ( π 2 ) = 0
L = lim x 2 cos ( π x ) cos ( π 2 ) x 2 = lim x 2 ϕ ( x ) ϕ ( 2 ) x 2 = ϕ ( 2 ) = π 2 2 sin ( π 2 )

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