(6)
Evaluate the lim
x tends to x/2
(1- sinx / sin x + cos 2x )
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Answered by
1
Answer:
gcujvoofdw68909544786587599
Answered by
1
Answer:
Let us multiply the numerator and denominator of (1 - cos x) / x by (1 + cos x) and write
limx→0 (1 - cos x) / x
= limx→0 [ (1 - cos x) / x ] *[ (1 + cos x) / (1 + cos x) ]
The numerator becomes 1 - cos 2 x = sin 2 x, hence
limx→0 (1 - cos x) / x
= limx→0 [ (sin 2 x) / x ] *[ 1/ (1 + cos x) ]
The limit can be written
limx→0 (1 - cos x) / x
= limx→0 [ (sin x) / x ] * limx→0 [ sin x / (1 + cos x) ] = (1)(0/2) = 0
We have used the theorem: limx→0 [ (sin x) / x ] = 1
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