evaluate limit x-> 0. (x tan x) / (1 - cos 2x)
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Answer is attached as an image with the reasons and proper steps.
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Sabya1:
good answer
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Dear answer = 1/2
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Lim(x→0) {xtanx}/(1 - cos2x )
we know,
(1 - cos2x) =2sin²x ,
use this here,
Lim(x→0){xtanx}/(2sin²x)
=1/2 × Lim(x→0){ x ×( tanx/x)× x }/(sinx/x)² ×x²
we know,
Lim(f(x) →0) tanf(x)/f(x) = 1
Lim(f(x)→0) sinf(x)/f(x) = 1
use this concept now,
= 1/2 × Lim(x→0) { x²/x²}
= 1/2 × 1
= 1/2 ( answer )
we know,
(1 - cos2x) =2sin²x ,
use this here,
Lim(x→0){xtanx}/(2sin²x)
=1/2 × Lim(x→0){ x ×( tanx/x)× x }/(sinx/x)² ×x²
we know,
Lim(f(x) →0) tanf(x)/f(x) = 1
Lim(f(x)→0) sinf(x)/f(x) = 1
use this concept now,
= 1/2 × Lim(x→0) { x²/x²}
= 1/2 × 1
= 1/2 ( answer )
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