Limit By Applying L'Hopital'S Rule Whenever Possible?
1. lim cot x / cot 2x
x>0
2. lim cosec 6x / cosec 2x
x>/2
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1. lim cot x / cot 2x
x>0
2. lim cosec 6x / cosec 2x
x>π/2
-Anonymous
x>0
2. lim cosec 6x / cosec 2x
x>π/2
1. Note that:
cot(x)/cot(2x) = tan(2x)/tan(x)
Then..
lim x→0 tan(2x)/tan(x) = 2
2. lim x→π/2 csc(6x)/csc(2x)
Note that csc(6x)/csc(2x) = sin(2x)/sin(6x). Then..
lim x→0 sin(2x)/sin(6x) = 2/6 = 1/3
I hope this hleps!
-Anonymous
cot(x)/cot(2x) = tan(2x)/tan(x)
Then..
lim x→0 tan(2x)/tan(x) = 2
2. lim x→π/2 csc(6x)/csc(2x)
Note that csc(6x)/csc(2x) = sin(2x)/sin(6x). Then..
lim x→0 sin(2x)/sin(6x) = 2/6 = 1/3
I hope this hleps!
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