How do you find the limit of (sin(x^2))/x as theta rightarrow 0?

Ressuli422p

Ressuli422p

Answered question

2023-03-22

How to find the limit of sin ( x 2 ) x as θ 0 ?

Answer & Explanation

svalan7rkp

svalan7rkp

Beginner2023-03-23Added 6 answers

Answer is Reqd. Lim. = 0 .
Solution: Reqd. Lim. = lim x 0 sin ( x 2 ) x
= lim x 0 ( sin x 2 x 2 ) ( x 2 x )
= lim x 0 ( sin x 2 x 2 ) ( x )
= { lim θ 0 sin θ θ } { lim x 0 x }
where, θ = x 2 , and, as x 0 , θ 0 . ]
= ( 1 ) ( 0 )
Reqd. Lim. = 0 .

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